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Celebratio Mathematica

Michael H. Freedman

Topology; quantum computing  ·  UCSD & Microsoft

Topology in dImension 4

[1] article M. H. Freed­man and L. Taylor: “\( \Lambda \)-split­ting 4-man­i­folds,” To­po­logy 16 : 2 (1977), pp. 181–​184. MR 0442954 Zbl 0363.​57004

[2] incollection M. Freed­man and R. Kirby: “A geo­met­ric proof of Roch­lin’s the­or­em,” pp. 85–​97 in Al­geb­ra­ic and geo­met­ric to­po­logy (Stan­ford Uni­versity, CA, Au­gust 2–21, 1976), part 2. Edi­ted by R. J. Mil­gram. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics XXXII. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1978. MR 0520525 Zbl 0392.​57018

[3] article M. H. Freed­man: “Quad­ruple points of 3-man­i­folds in \( S^{4} \),” Com­ment. Math. Helv. 53 : 3 (1978), pp. 385–​394. MR 0505553 Zbl 0404.​57011

[4] article M. H. Freed­man: “A fake \( S^{3}\times \mathbf{R} \),” Ann. of Math. (2) 110 : 1 (1979), pp. 177–​201. MR 0541336 Zbl 0442.​57014

[5] article M. H. Freed­man: “A con­verse to (Mil­nor–Ker­vaire the­or­em)\( \times R \) etc…,” Pa­cific J. Math. 82 : 2 (1979), pp. 357–​369. MR 0551695 Zbl 0459.​57020

[6] article M. H. Freed­man: “Can­cel­ling 1-handles and some to­po­lo­gic­al im­bed­dings,” Pa­cific J. Math. 80 : 1 (1979), pp. 127–​130. MR 0534700 Zbl 0416.​57016

[7] incollection L. Sieben­mann: “Amorces de la chirur­gie en di­men­sion quatre: un \( S^{3}\times \mathbf{R} \) exotique [d’après An­drew J. Cas­son et Mi­chael H. Freed­man],” pp. 183–​207 in Sémin­aire Bourbaki (1978/79). Lec­ture Notes in Math­em­at­ics 770. Spring­er (Ber­lin), 1980. Ex­posé no. 536. MR 572425 Zbl 0444.​57021

[8] article M. Freed­man and F. Quinn: “A quick proof of the 4-di­men­sion­al stable sur­gery the­or­em,” Com­ment. Math. Helv. 55 : 4 (1980), pp. 668–​671. MR 0604722 Zbl 0453.​57024

[9]M. H. Freed­man: [Un­pub­lished hand­writ­ten notes].

[10] article M. Freed­man and F. Quinn: “Slightly sin­gu­lar 4-man­i­folds,” To­po­logy 20 : 2 (1981), pp. 161–​173. MR 0605655 Zbl 0459.​57008

[11] article M. H. Freed­man: “A sur­gery se­quence in di­men­sion four; the re­la­tions with knot con­cord­ance,” In­vent. Math. 68 : 2 (1982), pp. 195–​226. MR 0666159 Zbl 0504.​57016

[12] article M. Freed­man, J. Hass, and P. Scott: “Closed geodesics on sur­faces,” Bull. Lon­don Math. Soc. 14 : 5 (1982), pp. 385–​391. MR 0671777 Zbl 0476.​53026

[13] article M. H. Freed­man: “The to­po­logy of four-di­men­sion­al man­i­folds,” J. Dif­fer­en­tial Geom. 17 : 3 (1982), pp. 357–​453. MR 0679066 Zbl 0528.​57011

[14]M. Freed­man and K. Uh­len­beck: Gauge the­or­ies and four-man­i­folds. Technical report 025-83, U.C. Berke­ley, 1983. Notes by D. Freed and K. Uh­len­beck.

[15] incollection M. H. Freed­man: “The disk the­or­em for four-di­men­sion­al man­i­folds,” pp. 647–​663 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Au­gust 16–24, 1983, Warsaw), vol. 1. Edi­ted by Z. Ciesiel­ski and C. Olech. PWN (Warsaw), 1984. MR 0804721 Zbl 0577.​57003

[16] article M. H. Freed­man: “There is no room to spare in four-di­men­sion­al space,” No­tices Amer. Math. Soc. 31 : 1 (1984), pp. 3–​6. MR 0728340 Zbl 0538.​57001

[17] incollection A. Cas­son and M. Freed­man: “Atom­ic sur­gery prob­lems,” pp. 181–​199 in Four-man­i­fold the­ory (Durham, NH, Ju­ly 4–10, 1982). Edi­ted by C. Gor­don and R. C. Kirby. Con­tem­por­ary Math­em­at­ics 35. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1984. MR 0780579 Zbl 0559.​57008

[18] article M. H. Freed­man and L. R. Taylor: “A uni­ver­sal smooth­ing of four-space,” J. Dif­fer­en­tial Geom. 24 : 1 (1986), pp. 69–​78. MR 0857376 Zbl 0586.​57007

[19] incollection M. H. Freed­man: “A geo­met­ric re­for­mu­la­tion of 4-di­men­sion­al sur­gery,” pp. 133–​141 in Spe­cial volume in hon­or of R. H. Bing (1914–1986), published as To­po­logy Ap­pl. 24 : 1–​3 (1986). MR 0872483 Zbl 0898.​57005

[20] incollection M. H. Freed­man: “Are the Bor­romean rings \( A \)-\( B \)-slice?,” pp. 143–​145 in Spe­cial volume in hon­or of R. H. Bing (1914–1986), published as To­po­logy Ap­pl. 24 : 1–​3. El­sevi­er Sci­ence B.V. (North-Hol­land) (Am­s­ter­dam), 1986. MR 0872484 Zbl 0627.​57004

[21] article M. H. Freed­man: “Poin­caré trans­vers­al­ity and four-di­men­sion­al sur­gery,” To­po­logy 27 : 2 (1988), pp. 171–​175. MR 0948180 Zbl 0654.​57007

[22] article M. H. Freed­man and X.-S. Lin: “On the \( (A,B) \)-slice prob­lem,” To­po­logy 28 : 1 (1989), pp. 91–​110. MR 0991101 Zbl 0845.​57016

[23] book M. H. Freed­man and F. Quinn: To­po­logy of 4-man­i­folds. Prin­ceton Math­em­at­ic­al Series 39. Prin­ceton Uni­versity Press (Prin­ceton, NJ), 1990. MR 1201584 Zbl 0705.​57001

[24] article S. De Michel­is and M. H. Freed­man: “Un­count­ably many exot­ic \( \mathbf{R}^ 4 \)’s in stand­ard 4-space,” J. Dif­fer­en­tial Geom. 35 : 1 (1992), pp. 219–​254. MR 1152230 Zbl 0780.​57012

[25] incollection M. H. Freed­man: “Work­ing and play­ing with the 2-disk,” pp. 37–​47 in Math­em­at­ics in­to the twenty-first cen­tury: Pro­ceed­ings of the 1988 Centen­ni­al Sym­posi­um (Provid­ence, RI, Au­gust 8–12, 1988). Edi­ted by F. E. Browder. Amer­ic­an Math­em­at­ic­al So­ci­ety Centen­ni­al Pub­lic­a­tions II. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1992. MR 1184613 Zbl 0924.​57026

[26] article M. H. Freed­man: “Link com­pos­i­tions and the to­po­lo­gic­al slice prob­lem,” To­po­logy 32 : 1 (1993), pp. 145–​156. MR 1204412 Zbl 0782.​57010

[27] article M. H. Freed­man and Z. Wang: “\( \mathbf{C}P^ 2 \)-stable the­ory,” Math. Res. Lett. 1 : 1 (1994), pp. 45–​48. MR 1258488 Zbl 0849.​57016

[28] article M. H. Freed­man, V. S. Krushkal, and P. Teich­ner: “Van Kampen’s em­bed­ding ob­struc­tion is in­com­plete for 2-com­plexes in \( \mathbf{R}^ 4 \),” Math. Res. Lett. 1 : 2 (March 1994), pp. 167–​176. MR 1266755 Zbl 0847.​57005

[29] article M. H. Freed­man and P. Teich­ner: “4-man­i­fold to­po­logy I: Subex­po­nen­tial groups,” In­vent. Math. 122 : 3 (1995), pp. 509–​529. MR 1359602 Zbl 0857.​57017

[30] article M. H. Freed­man and P. Teich­ner: “4-Man­i­fold to­po­logy II: Dwyer’s fil­tra­tion and sur­gery ker­nels,” In­vent. Math. 122 : 1 (1995), pp. 531–​557. MR 1359603 Zbl 0857.​57018

[31] article C. L. Curtis, M. H. Freed­man, W. C. Hsiang, and R. Stong: “A de­com­pos­i­tion the­or­em for \( h \)-cobord­ant smooth simply-con­nec­ted com­pact 4-man­i­folds,” In­vent. Math. 123 : 2 (1996), pp. 343–​348. MR 1374205 Zbl 0843.​57020

[32] article M. H. Freed­man, A. Kit­aev, C. Nayak, J. K. Slinger­land, K. Walk­er, and Z. Wang: “Uni­ver­sal man­i­fold pair­ings and pos­it­iv­ity,” Geom. To­pol. 9 (2005), pp. 2303–​2317. MR 2209373 Zbl 1129.​57035 ArXiv math/​0503054

[33] techreport M. Freed­man: Quantum grav­ity via man­i­fold pos­it­iv­ity. Pre­print, August 2010. ArXiv 1008.​1045

[34] article M. Freed­man, R. Gom­pf, S. Mor­ris­on, and K. Walk­er: “Man and ma­chine think­ing about the smooth 4-di­men­sion­al Poin­caré con­jec­ture,” Quantum To­pol. 1 : 2 (2010), pp. 171–​208. MR 2657647 Zbl 1236.​57043