Allen Hatcher

Allen Hatcher ( born 1944 in Indianapolis ) is an American mathematician who deals with geometric topology.

Hatcher was in 1971 with Hans Samelson at Stanford University PhD (A obstruction to pseudo- isotopies ). He was an associate professor at the University of California, Los Angeles, and since 1983 professor at Cornell University.

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

In 1983 he proved a conjecture of Stephen Smale (1959 ) via the diffeomorphisms group of the 3- sphere. He classified incompressible surfaces in various 3-manifolds, among others, William Floyd in bundles of punctured tori above 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 of (1980). He also worked on pseudo - isotopy and K- theory.

He is (provided partially online available by him ) as well as a writer of textbooks known topology.

Writings

• Algebraic Topology, Cambridge University Press 2002
• With John Wagoner pseudo - isotopies of compact manifolds, Société 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, p 373-377.
• With William Floyd Incompressible surfaces in punctured - torus bundles, Topology and its Applications, Volume 13, 1982, p 263-282.
• A proof of the Smale conjecture, Annals of Mathematics, Volume 117, 1983, pp. 553-607.
• With Thurston Incompressible surfaces in 2 -bridge knot complements, Inventiones Mathematicae, Volume 79, 1985, p 225-246

Homepage

• Homepage at Cornell University
• Website with its online books