Celebratio Mathematica

Martin Scharlemann

Martin George Scharlemann

by Rob Kirby

Marty Schar­le­mann was born on 6 Decem­ber 1948 on an air force base in Carl­isle, Pennsylvania.

His fath­er, Mar­tin H. Schar­le­mann, born in Illinois in 1910, had a Ph.D. in clas­sic­al lan­guages from Wash­ing­ton Uni­versity in St. Louis and was a chap­lain in the Air Force dur­ing World War II, and later rose to the rank of Bri­gadier Gen­er­al — not a usu­al as­cent for a chap­lain! Marty’s grand­fath­er, Ernst Schar­le­mann, was also a Luther­an min­is­ter as well as a one-time politi­cian who ran for Sen­at­or while liv­ing in Min­nesota. He lost, but he per­suaded his flock to vote Farm­er–Labor in a cru­cial elec­tion, and his dis­trict was re­war­ded with one of the first four-lane di­vided high­ways in the US. It only ran for 1.5 miles, and has since been al­lowed to de­gen­er­ate to a mere two lanes as something of a “road to nowhere”. Ernst had emig­rated from Schleswig-Hol­stein, just south of Den­mark, and settled in a Ger­man speak­ing colony in the US. Marty’s fath­er grew up speak­ing Ger­man and learned Eng­lish as a second lan­guage. After World War II he be­came a pro­fess­or at Con­cor­dia Sem­in­ary in St. Louis where Marty grew up. So, like Ger­man Chan­cel­lor An­gela Merkel, Marty grew up on the grounds of a Luther­an sem­in­ary where his fath­er was a pro­fess­or.

In 1938 Marty’s fath­er mar­ried Dorothy Hoy­er, the daugh­ter of a pro­fess­or at the same sem­in­ary whose fam­ily had emig­rated from Ger­many be­fore the Amer­ic­an Civil War. They had four chil­dren: Edith who taught in a ju­ni­or col­lege; Ted who is a phys­i­cist at Liv­er­more Lab; Marty, the math­em­atician; and John who be­came a Luther­an min­is­ter.

Marty went to Luther­an pa­ro­chi­al schools and had ex­cel­lent teach­ers. He left high-school after three years (hav­ing sat­is­fied all but his PE re­quire­ments!) and ma­tric­u­lated at Prin­ceton Uni­versity in 1965. There he in­ten­ded to ma­jor in phys­ics un­til in 1966–67 he took an hon­ors cal­cu­lus course us­ing Mi­chael Spivak’s book Cal­cu­lus on Man­i­folds; Den­nis Sul­li­van was such an in­spir­ing teach­er that Marty switched from phys­ics to math.

His ju­ni­or thes­is was ad­vised by Mar­shall Co­hen (who later spent a long ca­reer in to­po­logy at Cor­nell). Ral­ph Fox was Marty’s ad­viser for his seni­or thes­is. Fox was giv­ing a course in shape the­ory and sug­ges­ted that top­ic to Marty and told him to read Steen­rod’s book [◊] on fiber bundles.

After a while, Fox men­tioned a prob­lem that he had in mind for Marty. It was known that the cov­er­ing spaces for \( X \) were de­term­ined by the shape of \( X \). (Here \( X \) is a sep­ar­able met­ric space in \( \mathbb{R}^N \) and its shape is the in­verse lim­it of neigh­bor­hoods of \( X \subset \mathbb{R}^N \).) Fox asked Marty to prove the same for fiber bundles over \( X \).

Late in the year Fox asked Marty how he was do­ing and Marty said he had a counter­example. Fox asked what the group (of the bundle) was and Marty, think­ing mul­ti­plic­at­ively, said the pos­it­ive ra­tion­als. Fox thought ad­dit­ively and said, “But that’s not a group!”. Both mo­ment­ar­ily wore hor­ri­fied ex­pres­sions.

Marty went off to Berke­ley in 1969 and took his Ph.D. quals in 1970. The qual sys­tem at Berke­ley then was to take three one-hour or­al ex­ams on a Sat­urday. Marty did well in to­po­logy and ana­lys­is but not al­gebra. The dis­ap­poin­ted ex­am­iners asked if it had been hard to study in the wake of Nix­on’s Cam­bod­i­an in­va­sion. Marty said, “Yes!” (When they throw you a life­line, grab it!)

In 1971, Marty asked Emery Thomas to be his Ph.D. ad­viser, but Thomas was go­ing on sab­bat­ic­al. So he asked Tom Far­rell who’d taught a ter­rif­ic course, but it turned out Far­rell was leav­ing Berke­ley. Then he tried Low­ell Jones, but same prob­lem. Fi­nally he heard that I was com­ing to Berke­ley in 1971–72 so he waited un­til the first day I ar­rived in Janu­ary 1972, and I said yes.

Dur­ing Marty’s second year, he met Bar­bara Wag­n­er, a seni­or in psy­cho­logy, at folk dan­cing. They mar­ried in 1974. She got a teach­ing cre­den­tial at Berke­ley and later worked in the Cali­for­nia Em­ploy­ment De­vel­op­ment De­part­ment. They have a daugh­ter, Tess. She is a Ph.D. eco­nom­ist who has worked with the Coun­cil of Eco­nom­ic Ad­visers, the Treas­ury De­part­ment and now the Fed­er­al Re­serve.

Marty fin­ished his Ph.D. in 1974 with five pa­pers, pub­lished or sub­mit­ted. Prob­ably the best of these is his pa­per on to­po­lo­gic­al trans­vers­al­ity in di­men­sion four [◊] in which he gets as close as was pos­sible at that time to show­ing via trans­vers­al­ity that there is a to­po­lo­gic­al, al­most par­al­lel­iz­able, 4-man­i­fold with sig­na­ture 8 (this was fi­nally achieved by Freed­man in 1981).

Larry Sieben­mann had vis­ited Berke­ley in sum­mer 1973 and a col­lab­or­a­tion with Marty led to two pa­pers (of the afore­men­tioned five) con­cern­ing the Hauptver­mu­tung: [◊] and [◊]. The first shows that (avoid­ing di­men­sion 4) if a homeo­morph­ism between two smooth man­i­folds is a \( C^{\infty} \) map in one dir­ec­tion, then it is iso­top­ic to a PL-homeo­morph­ism. The second con­tains an in­ter­est­ing ex­ample, namely a homeo­morph­ism from a Brieskorn–Pham man­i­fold to \( \mathbb{RP}^5 \) which is not iso­top­ic to a \( C^{\infty} \) homeo­morph­ism.

While a gradu­ate stu­dent, Marty un­der­stood Markov’s pa­per [◊] show­ing that there can­not be an al­gorithm which will dis­tin­guish any two closed com­pact PL 4-man­i­folds. In a re­cent con­ver­sa­tion (\( \sim \)2014), Marty dredged up his re­col­lec­tions of 40 years earli­er and I wrote up his ex­pos­i­tion. I don’t know of any bet­ter ex­pos­i­tion, so I in­clude it in this volume.

Marty took a post doc­tor­al year at the In­sti­tute for Ad­vanced Study in 1974–75 and fol­lowed that with a year at the Uni­versity of Geor­gia. The lat­ter was fine math­em­at­ic­ally, but an op­por­tun­ity arose to move to the Uni­versity of Cali­for­nia, Santa Bar­bara, and that brought Marty and Barb to Cali­for­nia, which they loved.

While at UC­SB, Marty proved to be an ex­cel­lent ad­viser, as seen in his list of Ph.D. stu­dents. He served with dis­tinc­tion as Chair of the Math De­part­ment for three years, and then for an­oth­er year as in­ter­im chair. He bought a sports car, a BMW Z3, as a re­ward to him­self for agree­ing to be Chair. Later he served for three years on CAP, the cam­pus-wide Com­mit­tee on Aca­dem­ic Per­son­nel, and was Chair for the last year. With­in the Uni­versity of Cali­for­nia sys­tem, this com­mit­tee is the most im­port­ant one. He also served a term as Charges Of­ficer at UC­SB.

Marty and Bob Oliv­er were the found­ing ed­it­ors of Al­geb­ra­ic & Geo­met­ric To­po­logy, help­ing make it a great suc­cess story.