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Allen Hatcher | |
Born | October 23, 1944 (age 74) |
---|---|
Nationality | American |
Alma mater | Stanford University |
Scientific career | |
Fields | Mathematics |
Institutions | Cornell University |
Doctoral advisor | Hans Samelson |
Allen Edward Hatcher (born October 23, 1944) is an Americantopologist. Creative mediasource windows 10.
Gebraic topology into a one quarter course, but we were overruled by the analysts and algebraists, who felt that it was unacceptable for graduate students to obtain their PhDs without having some contact with algebraic topology. This raises a conundrum. A large number of students at Chicago go into topol-ogy, algebraic and geometric. Topology and H 1(U) is the union of open sets of the form W X W I containing x I. Since I is compact, by Tube Lemma W X W I contains a tube V I about x I where V is a neighborhood of x. So the restriction of Hon V Iis a map from V Ito U. Let i: V,!Ube an inclusion.
- 2Mathematical contributions
- 3Selected publications
- 3.2Books
Biography[edit]
Hatcher received his Ph.D. Melody tamil songs mp3 download. under the supervision of Hans Samelson at Stanford University in 1971. He went on to become a professor at the University of California, Los Angeles. Since 1983 he has been a professor at Cornell University.
Mathematical contributions[edit]
He has worked in geometric topology, both in high dimensions, relating pseudoisotopy to algebraic K-theory, and in low dimensions: surfaces and 3-manifolds, such as proving the Smale conjecture for the 3-sphere.
3-manifolds[edit]
![Topology Topology](/uploads/1/2/5/0/125071992/829653171.jpg)
Perhaps among his most recognized results in 3-manifolds concern the classification of incompressible surfaces in certain 3-manifolds and their boundary slopes. William Floyd and Hatcher classified all the incompressible surfaces in punctured-torus bundles over the circle. William Thurston and Hatcher classified the incompressible surfaces in 2-bridgeknotcomplements. As corollaries, this gave more examples of non-Haken, non-Seifert fibered, irreducible 3-manifolds and extended the techniques and line of investigation started in Thurston's Princeton lecture notes. Hatcher also showed that irreducible, boundary-irreducible 3-manifolds 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.
Introduction To Topology Pdf
Hatcher has made contributions to the so-called theory of essential laminations in 3-manifolds. He invented the notion of 'end-incompressibility' and several of his students, such as Mark Brittenham, Charles Delman, and Rachel Roberts, have made important contributions to the theory.
Surfaces[edit]
Hatcher and Thurston exhibited an algorithm to produce a presentation of the mapping class group of a closed, orientablesurface. Their work relied on the notion of a cut system and moves that relate any two systems.
Selected publications[edit]
Papers[edit]
- Allen Hatcher and William Thurston, A presentation for the mapping class group of a closed orientable surface,Topology19 (1980), no. 3, 221—237.
- Allen Hatcher, On the boundary curves of incompressible surfaces,Pacific Journal of Mathematics99 (1982), no. 2, 373—377.
- William Floyd and Allen Hatcher, Incompressible surfaces in punctured-torus bundles,Topology and its Applications13 (1982), no. 3, 263—282.
- Allen Hatcher and William Thurston, Incompressible surfaces in -bridge knot complements,Inventiones Mathematicae79 (1985), no. 2, 225—246.
- Allen Hatcher, A proof of the Smale conjecture, ,Annals of Mathematics (2) 117 (1983), no. 3, 553—607.
Books[edit]
- Hatcher, Allen, Algebraic topology. Cambridge University Press, Cambridge, 2002. xii+544 pp. ISBN0-521-79160-X and ISBN0-521-79540-0
Books in progress[edit]
External links[edit]
- Allen Hatcher at the Mathematics Genealogy Project
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