Richard Canary

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Richard Douglas Canary (* 1962 ) is an American mathematician who studies low-dimensional topology and Klein groups .

Canary studied at the New College of Florida with a bachelor's degree in mathematics in 1983, at the University of Warwick with a master's degree from David Epstein in 1985 ( A boys guide to William P. Thurston ) and was at Princeton University in 1989 with William Thurston PhD ( Hyperbolic structures on 3-manifolds with compressible boundaries ). From 1989 to 1991 he was Gabor Szegö Assistant Professor at Stanford University and from 1991 Assistant Professor, 1996 Associate Professor and 2001 Professor at the University of Michigan .

Canary is particularly concerned with hyperbolic manifolds in the tradition of the Thurston program .

With Jeffrey Brock and Yair Minsky he gave proof of the Ending Lamination Conjecture by Thurston in 2004 (also independently from Mary Rees )

He also dealt with applications of Tame Deities guess (tameness Conjecture) of Albert Marden (evidenced by Ian Agol , Danny Calegari , David Gabai 2004): he proved the Ahlfors presumption Klein groups in the case of topologically tame groups (1993), from which with the general Ahlfors conjecture follows the presumption of tameness (see Klein's group ).

Among other things, he was visiting scholar at the Institut Henri Poincaré , at the MSRI , at the Ecole Normale Superieure de Lyon, in Toulouse and at the University of Southampton .

From 1993 to 1997 he was a Sloan Research Fellow . He is a fellow of the American Mathematical Society .

He is the son of the English scholar Robert H. Canary (professor at the University of Wisconsin-Parkside ).

Fonts

  • Editor with David Epstein, Albert Marden Fundamentals of Hyperbolic Manifolds: Selected Expositions , London Mathematical Society Lecture Note Series 328, Cambridge University Press, 2006 (therein with Epstein, P. Green Notes on notes of Thurston , a reprint from 1987)
  • On the Laplacian and geometry of 3-manifolds , J. Differential Geometry, Volume 36, 1992, pp. 349-367
  • Covering theorems for hyperbolic 3-manifolds , Proceedings of Low-Dimensional Topology, International Press, 1994, 21-30.
  • A covering theorem for hyperbolic 3-manifolds and its applications , Topology, Volume 35, 1996, pp. 751-778.
  • Ends of hyperbolic 3-manifolds , Journal AMS, Volume 6, 1993, pp. 1-35
  • with Jim Anderson: Algebraic limits of Kleinian groups which rearrange the pages of a book. Invent. Math. 126 (1996) no. 2, 205-214.
  • Pushing the boundary , in In the tradition of Ahlfors and Bers III , Contemporary Mathematics 355, 2004, pp. 109–121
  • with Minsky On limits of tame hyperbolic 3-manifolds , J. Diff. Geom., Vol. 43, 1996, pp. 1-41
  • with Jim Anderson, Darryl McCullough On the topology of deformation spaces of Kleinian groups , Annals of Mathematics, Volume 152, 2000, pp. 693-741
  • with McCullough Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups , Memoirs AMS 172, 2004
  • with Brock, Minsky: The classification of Kleinian surface groups, II: The ending lamination conjecture. Ann. of Math. (2) 176 (2012), no. 1, 1-149.
  • with Bridgeman, Labourie, Sambarino: The pressure metric for Anosov representations. Geom. Funct. Anal. 25 (2015), no. 4, 1089–1179.

Web links

Individual evidence

  1. Brock, Canary, Minsky The classification of Kleinian surface groups II: the ending lamination conjecture , Annals of Mathematics, 176 (2012), 1--149, Arxiv
  2. Canary Marden's Tameness Conjecture: history and applications , in L. Ji, K. Liu, L. Yang, Shing-Tung Yau Geometry, Analysis and Topology of Discrete groups , Higher Education Press, 2008, pp. 137--162
  3. Canary Ends of hyperbolic 3-manifolds , Journal of the American Mathematical Society 6, 1993, 1-35
  4. This refers to Thurston Three dimensional geometry and topology , then only accessible to a limited extent, now available at http://library.msri.org/books/gt3m/ , the first chapters were published in 1997 by Thurston at Princeton University Press.