Allen hatcher

Allen Hatcher (* 1944 in Indianapolis ) is an American mathematician who studies geometric topology.

Allen hatcher

Hatcher received his doctorate in 1971 under Hans Samelson at Stanford University ( A obstruction to pseudo-isotopies ${\ displaystyle K_ {2}}$ ). He was an associate professor at the University of California, Los Angeles , and has been a professor at Cornell University since 1983 . In 1976 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ).

In 1975/76 and 1979/80 he was at the Institute for Advanced Study .

In 1983 he proved a conjecture by Stephen Smale (1959) about the diffeomorphism group of the 3-sphere . He classified incompressible surfaces in different 3-manifolds , among others with William Floyd in bundles of dotted tori over the circle and with William Thurston in 2-bridge knot complements. With Thurston he gave an algorithm for the presentation of the mapping class group of closed orientable surfaces (1980). He also worked on pseudo-isotopy and K-theory .

He is also known as the author of topology textbooks (some of which he has made available online).

Fonts

Algebraic Topology , Cambridge University Press 2002
with John Wagoner Pseudo-isotopies of compact manifolds , Societé Mathématiques de France, 1973
Higher simple homotopy theory , Annals of Mathematics, Volume 102, 1975, pp. 101-137.
with Thurston A presentation for the mapping class group of a closed orientable surface , Topology, Volume 19, 1980, pp. 221-237.
On the boundary curves of incompressible surfaces , Pacific J. Math., Vol. 99, 1982, pp. 373-377.
with William Floyd Incompressible surfaces in punctured-torus bundles , Topology and its Applications, Volume 13, 1982, pp. 263-282.
A proof of the Smale conjecture ${\ displaystyle \ mathrm {Diff} (S ^ {3}) \ simeq {\ mathrm {O}} (4)}$ ,, Annals of Mathematics, Volume 117, 1983, pp. 553-607.
with Thurston Incompressible surfaces in 2-bridge knot complements , Inventiones Mathematicae, Volume 79, 1985, pp. 225-246

↑ Dates of birth according to the membership book of the Institute for Advanced Studies 1980
^ Mathematics Genealogy Project
↑ That this is of the homotopy type of its isometric group, the orthogonal 4-dimensional group O (4)