James W. Cannon

James Weldon Cannon ( born January 30, 1943 in Bellefonte, Pennsylvania) is an American mathematician who deals with hyperbolic manifolds, geometric topology and geometric group theory.

Cannon in 1969 when Edmund Cecil Burgess at the University of Utah PhD ( Tame subsets of 2 - spheres in euclidean 3 -space ). From 1977 he was a professor at the University of Wisconsin -Madison and in 1986 at Brigham Young University.

In the 1970s, he released the double -suspension problem by John Milnor, by proving that the double hanging ( suspension ) of a homology sphere is a topological sphere. In 1979 he proved with Bryant and Larcher "almost" the characterization of topological manifolds hypothesis - manifolds in five or more dimensions that are meet the disjoint disks property topological manifolds (the proof was completed in 1983 by Frank Quinn ). Cannon was about before at the International Congress of Mathematicians in 1978.

In the 1980s he turned to hyperbolic 3-manifolds, Kleinian groups and geometric group theory. He examined combinatorial properties of Cayley graphs small shear groups and their relation to geometric properties of the operation of these groups in hyperbolic manifolds. In 1992, he was with Thurston and other one of the co - authors of a book on automatic groups, ie, geometric group theory on computational aspects.

In 1994 he proved a combinatorial version of him of the Riemann mapping theorem called theorem of geometric group theory. He gave necessary conditions to ensure that the operation of a group can be realized by homeomorphisms of a 2-sphere as Möbius transformations of the Riemann sphere. It explained in more subtle combinatorial subdivisions of the 2-sphere by order in the limit introduce a conformal geometry. A related context presumption of Cannon (1998) asks for the characterization of hyperbolic groups with 2-sphere as boundary, what Cannon has worked with William Floyd and Walter Parry (Introduction of finite subdivision rules), but also impact on the research other mathematicians had. Cannon, Floyd and Parry turned their work on finite subdivision rules in biology at ( pattern formation in organisms).

In 2012 he became a Fellow of the American Mathematical Society. He was invited speaker at the International Congress of Mathematicians in Helsinki 1978 ( The characterization of topological manifolds of dimension).

Writings

  • Recognition trouble. What is a topological manifold? , Bulletin AMS, Volume 84, 1978, p 832-866, online
  • Shrinking cell -like decompositions of manifolds. Codimension three, Annals of Mathematics, Volume 110, 1979, pp. 83-112.
  • JL Bryant, RC Lacher The structure of generalized manifolds having nonmanifold set of trivial dimension, in: Geometric topology ( Proc. Georgia Topology Conf, Athens, Ga., 1977. ), Academic Press 1979, pp. 261-300
  • The combinatorial structure of cocompact discrete hyperbolic groups, Geometriae Dedicata, Volume 16, 1984, pp. 123-148
  • David Epstein, Derek F. Holt, Silvio Levy, Michael S. Paterson, William Thurston Word processing in groups, Boston: Jones and Bartlett Publishers, 1992
  • Almost convex groups, Geometriae Dedicata, Volume 22, 1987, p 197-210
  • The combinatorial Riemann mapping theorem, Acta Mathematica, Volume 173, 1994, pp. 155-234,
  • William Floyd, Walter Parry Finite subdivision rules, Conformal Geometry and Dynamics, Volume 5, 2001, pp. 153-196
  • With Floyd, Parry Crystal growth, biological cell growth and geometry, in Pattern Formation in Biology, Vision and Dynamics, World Scientific, 2000, pp. 65-82
  • William Thurston Group invariant Peano curves, Geometry & Topology, Volume 11, 2007, pp. 1315-1355 ( as preprint since the mid- 1980s, circulatory, Cannon- Thurston - figure)

Homepage

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Frank Quinn (mathematician) William Floyd (mathematician) Mike Paterson
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