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Allen E. Hatcher  

Born  
Nationality  American 
Alma mater  Oberlin College Stanford University 
Scientific career  
Fields  Mathematics 
Institutions  Princeton University University of California, Los Angeles Cornell University 
Thesis  A K_{2} Obstruction for PseudoIsotopies (1971) 
Doctoral advisor  Hans Samelson 
Doctoral students 
Allen Edward Hatcher (born October 23, 1944) is an American topologist.
Biography
Hatcher was born in Indianapolis, Indiana.^{[1]} After obtaining his B.S from Oberlin College in 1966, he went for his graduate studies to Stanford University, where he received his Ph.D. in 1971.^{[1]} His thesis, A K_{2} Obstruction for PseudoIsotopies, was written under the supervision of Hans Samelson.^{[2]} 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 went on to become a professor at the University of California, Los Angeles in 1977. From 1983 he has been a professor at Cornell University; he is now a professor emeritus.^{[3]}
In 1978 Hatcher was an invited speaker at the International Congresses of Mathematicians in Helsinki.
Mathematical contributions
He has worked in geometric topology, both in high dimensions, relating pseudoisotopy to algebraic Ktheory, and in low dimensions: surfaces and 3manifolds, such as proving the Smale conjecture for the 3sphere.
3manifolds
Perhaps among his most recognized results in 3manifolds concern the classification of incompressible surfaces in certain 3manifolds and their boundary slopes. William Floyd and Hatcher classified all the incompressible surfaces in puncturedtorus bundles over the circle. William Thurston and Hatcher classified the incompressible surfaces in 2bridge knot complements. As corollaries, this gave more examples of nonHaken, nonSeifert fibered, irreducible 3manifolds and extended the techniques and line of investigation started in Thurston's Princeton lecture notes. Hatcher also showed that irreducible, boundaryirreducible 3manifolds with toral boundary have at most "half" of all possible boundary slopes resulting from essential surfaces. In the case of one torus boundary, one can conclude that the number of slopes given by essential surfaces is finite.
Hatcher has made contributions to the socalled theory of essential laminations in 3manifolds. He invented the notion of "endincompressibility" and several of his students, such as Mark Brittenham, Charles Delman, and Rachel Roberts, have made important contributions to the theory.
Surfaces
Hatcher and Thurston exhibited an algorithm to produce a presentation of the mapping class group of a closed, orientable surface. Their work relied on the notion of a cut system and moves that relate any two systems.
Selected publications
Papers
 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 puncturedtorus bundles, Topology and its Applications 13 (1982), no. 3, 263–282.
 Allen Hatcher and William Thurston, Incompressible surfaces in 2bridge knot complements, Inventiones Mathematicae 79 (1985), no. 2, 225–246.
 Allen Hatcher, A proof of the Smale conjecture, , Annals of Mathematics (2) 117 (1983), no. 3, 553–607.
Books
 Hatcher, Allen (2002). Algebraic topology. Cambridge: Cambridge University Press. ISBN 052179160X.
Books in progress
 Hatcher, Allen. "Vector Bundles and KTheory".
 Hatcher, Allen. "Spectral Sequences in Algebraic Topology".
 Hatcher, Allen. "Basic Topology of 3Manifolds".
External links
References
 ^ ^{a} ^{b} ^{c} "Annual Report for the Fiscal Year July 1, 1979–June 30, 1980" (PDF). Institute for Advanced Study. 1980. p. 41. Retrieved January 3, 2021.
 ^ Allen Hatcher at the Mathematics Genealogy Project
 ^ "Allen Hatcher, Professor Emeritus". Department of Mathematics, Cornell University.