Celebratio Mathematica

P. Emery Thomas

Topology; number theory

Bibliography

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phdthesis E. Thomas: A gen­er­al­iz­a­tion of the Pon­trja­gin square co­homo­logy op­er­a­tion. Ph.D. thesis, Prin­ceton Uni­versity, 1955. Ad­vised by N. E. Steen­rod. Pub­lished (un­der a dif­fer­ent title) as Mem­oirs of the Amer­ic­an Math­em­at­ic­al So­ci­ety 27 (1957). See also Proc. Nat. Acad. Sci. U.S.A. 42:5 (1956).

E. Thomas: “A gen­er­al­iz­a­tion of the Pon­trja­gin square co­homo­logy op­er­a­tion,” Proc. Nat. Acad. Sci. U.S.A. 42 : 5 (May 1956), pp. 266–​269. See also the au­thor’s PhD thes­is (1955). MR 0079254 Zbl 0071.​16302 article

N. E. Steen­rod and E. Thomas: “Co­homo­logy op­er­a­tions de­rived from cyc­lic groups,” Com­ment. Math. Helv. 32 (1957), pp. 129–​152. MR 0092148 Zbl 0090.​39101 article

E. Thomas: The gen­er­al­ized Pon­trja­gin co­homo­logy op­er­a­tions and rings with di­vided powers. Mem­oirs of the Amer­ic­an Math­em­at­ic­al So­ci­ety 27. 1957. Re­pub­lic­a­tion (un­der a dif­fer­ent title) of the au­thor’s PhD thes­is (1955). MR 0099029 Zbl 0085.​37504 book

F. P. Peterson and E. Thomas: “A note on non-stable co­homo­logy op­er­a­tions,” Bol. Soc. Mat. Mex., II. Ser. 3 (1958), pp. 13–​18. MR 0105680 Zbl 0121.​39604 article

E. Thomas: “The gen­er­al­ized Pon­trja­gin co­homo­logy op­er­a­tions,” pp. 155–​158 in Sym­posi­um in­ter­nacion­al de to­po­lo­gía al­geb­ra­ica [In­ter­na­tion­al sym­posi­um on al­geb­ra­ic to­po­logy] (Mex­ico City, Au­gust 1956). Uni­ver­sid­ad Nacion­al Autónoma de México and UN­ESCO (Mex­ico City and Par­is), 1958. MR 0099028 Zbl 0123.​16104 incollection

E. Thomas: “The func­tion­al Pon­trja­gin co­homo­logy op­er­a­tions,” Bol. Soc. Mat. Mex., II. Ser. 3 (1958), pp. 19–​24. MR 0103460 Zbl 0121.​39701 article

I. James and E. Thomas: “Which Lie groups are ho­mo­topy-abeli­an?,” Proc. Nat. Acad. Sci. U.S.A. 45 : 5 (May 1959), pp. 737–​740. MR 0106465 Zbl 0085.​25801 article

E. Thomas: “On tensor products of \( n \)-plane bundles,” Arch. Math. Lo­gik Grundla­gen­forsch 10 : 1 (1959), pp. 174–​179. MR 0107234 Zbl 0192.​29501 article

E. Thomas: “The sus­pen­sion of the gen­er­al­ized Pon­trja­gin co­homo­logy op­er­a­tions,” Pac. J. Math. 9 : 3 (July 1959), pp. 897–​911. MR 0110098 Zbl 0121.​39603 article

S. Araki, I. M. James, and E. Thomas: “Ho­mo­topy-abeli­an Lie groups,” Bull. Am. Math. Soc. 66 : 4 (1960), pp. 324–​326. MR 0119207 Zbl 0152.​01103 article

E. Thomas: “A note on cer­tain poly­no­mi­al al­geb­ras,” Proc. Am. Math. Soc. 11 : 3 (1960), pp. 410–​414. MR 0121393 Zbl 0098.​36201 article

E. Thomas: “On the co­homo­logy of the real Grass­mann com­plexes and the char­ac­ter­ist­ic classes of \( n \)-plane bundles,” Trans. Am. Math. Soc. 96 : 1 (July 1960), pp. 67–​89. MR 0121800 Zbl 0098.​36301 article

E. Thomas: “On func­tion­al cup-products and the trans­gres­sion op­er­at­or,” Arch. Math. 12 : 1 (1961), pp. 435–​444. MR 0149485 Zbl 0101.​15705 article

W. Browder and E. Thomas: “Ax­ioms for the gen­er­al­ized Pontry­agin co­homo­logy op­er­a­tions,” Q. J. Math., Oxf. II. Ser. 13 : 1 (1962), pp. 55–​60. MR 0140103 Zbl 0104.​39701 article

I. James and E. Thomas: “Ho­mo­topy-abeli­an to­po­lo­gic­al groups,” To­po­logy 1 : 3 (1962), pp. 237–​240. MR 0149483 Zbl 0107.​40602 article

E. Thomas: “The tor­sion Pontry­agin classes,” Proc. Am. Math. Soc. 13 : 3 (1962), pp. 485–​488. MR 0141132 Zbl 0109.​16001 article

I. James and E. Thomas: “Ho­mo­topy-com­mut­ativ­ity in ro­ta­tion groups,” To­po­logy 1 : 2 (1962), pp. 121–​124. MR 0139167 Zbl 0114.​39204 article

E. Thomas: “On the co­homo­logy groups of the clas­si­fy­ing space for the stable spinor groups,” Bol. Soc. Mat. Mex., II. Ser. 7 (1962), pp. 57–​69. MR 0153027 Zbl 0124.​16401 article

I. James and E. Thomas: “On ho­mo­topy-com­mut­ativ­ity,” Ann. Math. (2) 76 : 1 (July 1962), pp. 9–​17. MR 0139166 Zbl 0107.​40601 article

E. Thomas: “On the mod 2 co­homo­logy of cer­tain \( H \)-spaces,” Com­ment. Math. Helv. 37 (1962–1963), pp. 132–​140. MR 0149484 Zbl 0108.​35705 article

E. Thomas: “Steen­rod squares and \( H \)-spaces,” Ann. Math. (2) 77 : 2 (March 1963), pp. 306–​317. MR 0145526 Zbl 0115.​40303 article

I. M. James, E. Thomas, H. Toda, and G. W. White­head: “On the sym­met­ric square of a sphere,” J. Math. Mech. 12 : 5 (1963), pp. 771–​776. MR 0154282 Zbl 0136.​20301 article

W. Browder and E. Thomas: “On the pro­ject­ive plane of an \( H \)-space,” Ill. J. Math. 7 : 3 (1963), pp. 492–​502. MR 0151974 Zbl 0136.​43905 article

E. Thomas: “Ex­cep­tion­al Lie groups and Steen­rod squares,” Mich. Math. J. 11 : 2 (1964), pp. 151–​156. MR 0163307 Zbl 0136.​44001 article

E. Thomas: “Ho­mo­topy clas­si­fic­a­tion of maps by co­homo­logy ho­mo­morph­isms,” Trans. Am. Math. Soc. 111 : 1 (1964), pp. 138–​151. MR 0160212 Zbl 0119.​18401 article

E. Thomas: “On cross sec­tions to fiber spaces,” Proc. Nat. Acad. Sci. U.S.A. 54 : 1 (July 1965), pp. 40–​41. MR 0178476 Zbl 0132.​19701 article

I. James and E. Thomas: “An ap­proach to the enu­mer­a­tion prob­lem for non-stable vec­tor bundles,” J. Math. Mech. 14 : 3 (1965), pp. 485–​506. MR 0175134 Zbl 0142.​40701 article

E. Thomas: “Steen­rod squares and \( H \)-spaces, II,” Ann. Math. (2) 81 : 3 (May 1965), pp. 473–​495. MR 0177408 Zbl 0127.​13503 article

I. James and E. Thomas: “Note on the clas­si­fic­a­tion of cross-sec­tions,” To­po­logy 4 : 4 (January 1966), pp. 351–​359. MR 0212820 Zbl 0136.​44202 article

I. James and E. Thomas: “On the enu­mer­a­tion of cross-sec­tions,” To­po­logy 5 : 2 (May 1966), pp. 95–​114. MR 0196753 Zbl 0141.​40505 article

E. Thomas: “The Steen­rod squares in the mod two co­homo­logy al­gebra of an \( H \)-space,” pp. 113–​117 in Col­loque de to­po­lo­gie [To­po­logy sym­posi­um] (Brus­sels, 7–10 Septem­ber 1964). Pub­lic­a­tions du CBRM 22. Centre Belge de Recherches Math­ématiques (Liège), 1966. MR 0220276 Zbl 0136.​43904 incollection

E. Thomas: Sem­in­ar on fiber spaces (Berke­ley, 1964; Zürich, 1965). Lec­ture Notes in Math­em­at­ics 13. Spring­er (Ber­lin), 1966. MR 0203733 Zbl 0151.​31604 book

E. Thomas: “Cross-sec­tions of stably equi­val­ent vec­tor bundles,” Q. J. Math., Oxf. II. Ser. 17 : 1 (1966), pp. 53–​57. MR 0196747 Zbl 0135.​41301 article

E. Thomas: “An ex­act se­quence for prin­cip­al fibra­tions,” Bol. Soc. Mat. Mex., II. Ser. 12 (1967), pp. 35–​45. MR 0243526 Zbl 0183.​51702 article

E. Thomas: “Fields of tan­gent \( k \)-planes on man­i­folds,” In­vent. Math. 3 : 4 (1967), pp. 334–​347. MR 0217814 Zbl 0162.​55402 article

I. James and E. Thomas: “Sub­mer­sions and im­mer­sions of man­i­folds,” In­vent. Math. 2 : 3 (1967), pp. 171–​177. MR 0212821 Zbl 0146.​19803 article

E. Thomas: “The in­dex of a tan­gent 2-field,” Com­ment. Math. Helv. 42 (1967), pp. 86–​110. Ded­ic­ated to Pro­fess­or H. Hopf. MR 0215317 Zbl 0153.​53504 article

E. Thomas: “Com­plex struc­tures on real vec­tor bundles,” Am. J. Math. 89 : 4 (October 1967), pp. 887–​908. MR 0220310 Zbl 0174.​54802 article

E. Thomas: “Post­nikov in­vari­ants and high­er or­der co­homo­logy op­er­a­tions,” Ann. Math. (2) 85 : 2 (March 1967), pp. 184–​217. MR 0210135 Zbl 0152.​22002 article

E. Thomas: “Real and com­plex vec­tor fields on man­i­folds,” J. Math. Mech. 16 : 11 (1967), pp. 1183–​1205. MR 0210136 Zbl 0153.​53503 article

E. Thomas: “Fields of tan­gent 2-planes on even-di­men­sion­al man­i­folds,” Ann. Math. (2) 86 : 2 (September 1967), pp. 349–​361. MR 0212834 Zbl 0168.​21401 article

E. Thomas: “Sub­mer­sions and im­mer­sions with codi­men­sion one or two,” Proc. Am. Math. Soc. 19 : 4 (1968), pp. 859–​863. MR 0229246 Zbl 0169.​26102 article

E. Thomas: “Vec­tor fields on low di­men­sion­al man­i­folds,” Math. Z. 103 : 2 (1968), pp. 85–​93. MR 0224109 Zbl 0162.​55403 article

A. Hughes and E. Thomas: “A note on cer­tain sec­ond­ary co­homo­logy op­er­a­tions,” Bol. Soc. Mat. Mex., II. Ser. 13 (1968), pp. 1–​17. MR 0266203 Zbl 0207.​21801 article

E. Thomas: “The span of a man­i­fold,” Q.J. Math., Oxf. II. Ser. 19 : 1 (1968), pp. 225–​244. MR 0234487 Zbl 0167.​51901 article

D. Frank and E. Thomas: “A gen­er­al­iz­a­tion of the Steen­rod–White­head vec­tor field the­or­em,” To­po­logy 7 : 3 (August 1968), pp. 311–​316. MR 0229253 Zbl 0186.​57303 article

E. Thomas: “On the ex­ist­ence of im­mer­sions and sub­mer­sions,” Trans. Am. Math. Soc. 132 : 2 (1968), pp. 387–​394. MR 0225332 Zbl 0169.​26101 article

E. Thomas: “Vec­tor fields on man­i­folds,” Bull. Am. Math. Soc. 75 (1969), pp. 643–​683. MR 0242189 Zbl 0183.​51703 article

E. Thomas: “The Thom–Mas­sey ap­proach to em­bed­dings,” pp. 283–​307 in The Steen­rod al­gebra and its ap­plic­a­tions (Bat­telle Me­mori­al In­sti­tute, Colum­bus, OH, 30 March–4 April 1970). Edi­ted by F. P. Peterson. Lec­ture Notes in Math­em­at­ics 168. Spring­er (Ber­lin), 1970. Pro­ceed­ings of a con­fer­ence to cel­eb­rate N. E. Steen­rod’s six­tieth birth­day. MR 0287560 Zbl 0216.​45302 incollection

E. Thomas: “Whit­ney–Cartan product for­mu­lae,” Math. Z. 118 : 2 (1970), pp. 115–​138. MR 0278296 Zbl 0205.​53103 article

E. Thomas: “Some re­marks on vec­tor fields,” pp. 107–​113 in H-spaces: Act­es de la réunion de Neuchâtel [H-spaces: Pro­ceed­ings of the Neuchâtel meet­ing] (Neuchâtel, Switzer­land, Au­gust 1970). Edi­ted by F. Sigrist. Lec­ture Notes in Math­em­at­ics 196. Spring­er (Ber­lin), 1971. MR 0287567 Zbl 0218.​57013 incollection

incollection L. L. Lar­more and E. Thomas: “Group ex­ten­sions and prin­cip­al fibra­tions” in Pro­ceed­ings of the ad­vanced study in­sti­tute on al­geb­ra­ic to­po­logy (Aar­hus, Den­mark, 10–13 Au­gust 1970), vol. 2. Vari­ous pub­lic­a­tions series 13. Aar­hus Uni­versitet Matem­at­isk En­sti­tut, 1971. Also pub­lished as Math. Scand. 30 (1972).

L. L. Lar­more and E. Thomas: “Group ex­ten­sions and prin­cip­al fibra­tions,” Math. Scand. 30 (1972), pp. 227–​248. Also ap­peared in Pro­ceed­ings of the ad­vanced study in­sti­tute on al­geb­ra­ic to­po­logy (1970). MR 0328935 Zbl 0254.​55009 article

E. Thomas: “Co­homo­logy op­er­a­tions on \( p \)-fold sums,” Proc. Am. Math. Soc. 33 : 2 (June 1972), pp. 551–​553. MR 0290356 Zbl 0242.​55024 article

L. L. Lar­more and E. Thomas: “Map­pings in­to loop spaces and cent­ral group ex­ten­sions,” Math. Z. 128 : 4 (1972), pp. 277–​296. MR 0317318 Zbl 0254.​55010 article

E. Thomas: “Sec­ond­ary ob­struc­tions to in­teg­rabil­ity,” pp. 655–​661 in Dy­nam­ic­al sys­tems (Sal­vador, Brazil, 26 Ju­ly–14 Au­gust 1971). Edi­ted by M. M. Peix­oto. Aca­dem­ic Press (New York), 1973. MR 0343293 Zbl 0285.​58005 incollection

L. L. Lar­more and E. Thomas: “Group ex­ten­sions and twis­ted co­homo­logy the­or­ies,” Ill. J. Math. 17 : 3 (1973), pp. 397–​410. MR 0336744 Zbl 0274.​55022 article

J. Wood and E. Thomas: “On sig­na­tures as­so­ci­ated with rami­fied cov­er­ings and em­bed­ding prob­lems,” pp. 229–​235 in Col­loque in­ter­na­tion­al sur l’ana­lyse et la to­po­lo­gie différen­ti­elle [In­ter­na­tion­al sym­posi­um on ana­lys­is and dif­fer­en­tial to­po­logy] (CNRS, Stras­bourg, 20–29 June 1972), published as Ann. Inst. Four­i­er 23 : 2 (1973). Col­loques in­ter­na­tionaux du Centre na­tion­al de la recher­che sci­en­ti­fique 210. MR 0339201 Zbl 0262.​57012 incollection

E. Thomas and R. S. Zahler: “Non­tri­vi­al­ity of the stable ho­mo­topy ele­ment \( \gamma_1 \),” J. Pure Ap­pl. Al­gebra 4 : 2 (April 1974), pp. 189–​203. MR 0356049 Zbl 0287.​55014 article

R. Hartshorne, E. Rees, and E. Thomas: “Nonsmooth­ing of al­geb­ra­ic cycles on Grass­mann vari­et­ies,” Bull. Am. Math. Soc. 80 : 5 (September 1974), pp. 847–​851. MR 0357402 Zbl 0289.​14011 article

E. Thomas and J. Wood: “On man­i­folds rep­res­ent­ing ho­mo­logy classes in codi­men­sion 2,” In­vent. Math. 25 : 1 (1974), pp. 63–​89. MR 0383438 Zbl 0283.​57018 article

E. Thomas: “In­teg­ral­ity re­la­tions on smooth man­i­folds,” Math. Scand. 39 : 2 (1976), pp. 195–​231. MR 0442933 Zbl 0356.​57006 article

E. Thomas: “Em­bed­ding man­i­folds in Eu­c­lidean space,” Osaka J. Math. 13 : 1 (1976), pp. 163–​186. MR 0474332 Zbl 0328.​57009 article

E. Thomas and R. Zahler: “Gen­er­al­ized high­er or­der co­homo­logy op­er­a­tions and stable ho­mo­topy groups of spheres,” Adv. Math. 20 : 3 (June 1976), pp. 287–​328. MR 0423351 Zbl 0335.​55009 article

E. Rees and E. Thomas: “On the di­vis­ib­il­ity of cer­tain Chern num­bers,” Q. J. Math., Oxf. II. Ser. 28 : 4 (1977), pp. 389–​401. MR 0467771 Zbl 0401.​55009 article

E. Rees and E. Thomas: “Smooth­ings of isol­ated sin­gu­lar­it­ies,” pp. 111–​117 in Al­geb­ra­ic and geo­met­ric to­po­logy (Stan­ford, CA, 2–21 Au­gust 1976), part 2. Edi­ted by R. J. Mil­gram. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 32. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1978. MR 520527 Zbl 0398.​57001 incollection

E. Rees and E. Thomas: “Cobor­d­ism ob­struc­tions to de­form­ing isol­ated sin­gu­lar­it­ies,” Math. Ann. 232 : 1 (1978), pp. 33–​53. MR 0500994 Zbl 0381.​57011 article

E. Rees and E. Thomas: “Com­plex cobor­d­ism and in­ter­sec­tions of pro­ject­ive vari­et­ies,” pp. 168–​178 in Var­iétés ana­lytiques com­pact­es [Com­pact ana­lyt­ic vari­et­ies] (Nice, 19–23 Septem­ber 1977). Edi­ted by Y. Her­vi­er and A. Hirschow­itz. Lec­ture Notes in Math­em­at­ics 683. Spring­er (Ber­lin), 1978. MR 517524 Zbl 0427.​57016 incollection

E. Thomas: “Fun­da­ment­al units for or­ders in cer­tain cu­bic num­ber fields,” J. Reine An­gew. Math. 1979 : 310 (1979), pp. 33–​55. MR 546663 Zbl 0427.​12005 article

E. Thomas and A. T. Vasquez: “On the res­ol­u­tion of cusp sin­gu­lar­it­ies and the Shintani de­com­pos­i­tion in totally real cu­bic num­ber fields,” Math. Ann. 247 : 1 (1980), pp. 1–​20. MR 565136 Zbl 0403.​14005 article

L. L. Lar­more and E. Thomas: “On the fun­da­ment­al group of a space of sec­tions,” Math. Scand. 47 : 2 (1980), pp. 232–​246. MR 612697 Zbl 0463.​55010 article

E. Rees and E. Thomas: “Real­iz­ing ho­mo­logy classes by al­most-com­plex sub­man­i­folds,” Math. Z. 172 : 2 (1980), pp. 195–​201. MR 580860 Zbl 0443.​14010 article

E. Thomas and A. T. Vasquez: “Di­o­phant­ine equa­tions arising from cu­bic num­ber fields,” J. Num­ber The­ory 13 : 3 (August 1981), pp. 398–​414. MR 634208 Zbl 0468.​10009 article

E. Thomas and A. T. Vasquez: “Chern num­bers of Hil­bert mod­u­lar vari­et­ies,” J. Reine An­gew. Math. 1981 : 324 (1981), pp. 192–​210. MR 614525 Zbl 0491.​14019 article

E. Thomas and A. T. Vasquez: “Chern num­bers of cusp res­ol­u­tions in totally real cu­bic num­ber fields,” J. Reine An­gew. Math. 1981 : 324 (1981), pp. 175–​191. MR 614524 Zbl 0491.​14018 article

E. Thomas and A. T. Vasquez: “Betti num­bers of Hil­bert mod­u­lar vari­et­ies,” pp. 70–​87 in To­po­lo­gic­al top­ics: Art­icles on al­gebra and to­po­logy presen­ted to P. J. Hilton in cel­eb­ra­tion of his six­tieth birth­day. Edi­ted by I. M. James. Lon­don Math­em­at­ic­al So­ci­ety Lec­ture Note Series 86. Cam­bridge Uni­versity Press, 1983. MR 827249 Zbl 0523.​14026 incollection

E. Thomas: “De­fects of cusp sin­gu­lar­it­ies,” Math. Ann. 264 : 3 (1983), pp. 397–​411. MR 714112 Zbl 0504.​14002 article

E. Thomas and A. T. Vasquez: “Rings of Hil­bert mod­u­lar forms,” Com­pos. Math. 48 : 2 (1983), pp. 139–​165. MR 700001 Zbl 0515.​10027 article

E. Thomas: “On the zeta func­tion for func­tion fields over \( \mathbf{F}_p \),” Pac. J. Math. 107 : 1 (1983), pp. 251–​256. MR 701822 Zbl 0518.​12007 article

E. Thomas and A. T. Vasquez: “A fam­ily of el­lipt­ic curves and cyc­lic cu­bic field ex­ten­sions,” Math. Proc. Camb. Philos. Soc. 96 : 1 (July 1984), pp. 39–​43. MR 743699 Zbl 0555.​14010 article

E. Thomas: “Com­plete solu­tions to a fam­ily of cu­bic Di­o­phant­ine equa­tions,” J. Num­ber The­ory 34 : 2 (February 1990), pp. 235–​250. MR 1042497 Zbl 0697.​10011 article

E. Thomas: “Solu­tions to cer­tain fam­il­ies of Thue equa­tions,” J. Num­ber The­ory 43 : 3 (March 1993), pp. 319–​369. MR 1212687 Zbl 0774.​11013 article

E. Thomas: “Solu­tions to in­fin­ite fam­il­ies of com­plex cu­bic Thue equa­tions,” J. Reine An­gew. Math. 1993 : 441 (January 1993), pp. 17–​32. MR 1228609 Zbl 0780.​11014 article

E. Thomas: “Count­ing solu­tions to tri­no­mi­al Thue equa­tions: A dif­fer­ent ap­proach,” Trans. Am. Math. Soc. 352 : 8 (2000), pp. 3595–​3622. MR 1641119 Zbl 0995.​11025 article

E. Thomas: “Char­ac­ter­ist­ic classes and dif­fer­en­ti­able man­i­folds,” pp. 113–​187 in Classi car­at­ter­istiche e ques­tioni con­nesse [Char­ac­ter­ist­ic classes and re­lated ques­tions] (L’Aquila, Italy, 2–10 Septem­ber 1966). Edi­ted by E. Mar­tinelli. C.I.M.E. Sum­mer Schools 41. Spring­er (Heidel­berg), 2010. MR 2768044 incollection