Hatcher was born in Indianapolis, Indiana.^[1] After obtaining his B.A. and B.Mus. from Oberlin College in 1966,^[2] he went for his graduate studies to Stanford University, where he received his Ph.D. in 1971.^[1] His thesis, A K₂ Obstruction for Pseudo-Isotopies, was written under the supervision of Hans Samelson.^[3]

Afterwards, Hatcher went to Princeton University, where he was an NSF postdoc for a year, then a lecturer for another year, and then Assistant Professor from 1973 to 1979. He was also a member of the Institute for Advanced Study in 1975–76 and 1979–80.^[1] Hatcher moved to the University of California, Los Angeles as an assistant professor in 1977. From 1983 he has been a professor at Cornell University; he is now a professor emeritus.^[4]

In 1978 Hatcher was an invited speaker at the International Congress of Mathematicians in Helsinki.^[5]

In 1983 Hatcher proved the Smale conjecture, named after Stephen Smale.^[6][7]

• Allen Hatcher and William Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (1980), no. 3, 221–237.
• Allen Hatcher, On the boundary curves of incompressible surfaces, Pacific Journal of Mathematics 99 (1982), no. 2, 373–377.
• William Floyd and Allen Hatcher, Incompressible surfaces in punctured-torus bundles, Topology and its Applications 13 (1982), no. 3, 263–282.
• Allen Hatcher and William Thurston, Incompressible surfaces in 2-bridge knot complements, Inventiones Mathematicae 79 (1985), no. 2, 225–246.
• Allen Hatcher, A proof of the Smale conjecture, ${\displaystyle \mathrm {Diff} (S^{3})\simeq {\mathrm {O} }(4)}$ , Annals of Mathematics (2) 117 (1983), no. 3, 553–607.

• Hatcher, Allen (2002). Algebraic topology. Cambridge: Cambridge University Press. ISBN 0-521-79160-X.
• Hatcher, Allen. "Vector Bundles and K-Theory".
• Hatcher, Allen. "Spectral Sequences in Algebraic Topology".
• Hatcher, Allen. "Basic Topology of 3-Manifolds".
• Hatcher, Allen. "Topology of Numbers".

• "Hatcher's personal homepage".