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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of the Epstein-Penner construction to projective manifolds
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by D. Cooper and D. D. Long PDF
Proc. Amer. Math. Soc. 143 (2015), 4561-4569 Request permission

Abstract:

We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting.
References
  • R. D. Canary, D. B. A. Epstein, and P. Green, Notes on notes of Thurston, Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984) London Math. Soc. Lecture Note Ser., vol. 111, Cambridge Univ. Press, Cambridge, 1987, pp. 3–92. MR 903850
  • D. Cooper, D. D. Long and S. Tillmann, On convex projective manifolds and cusps, To appear Advances in Mathematics.
  • D. Cooper, D. D. Long and S. Tillmann, Deforming finite volume properly convex real projective manifolds, Preprint.
  • D. B. A. Epstein and R. C. Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988), no. 1, 67–80. MR 918457
  • Akira Ushijima, A canonical cellular decomposition of the Teichmüller space of compact surfaces with boundary, Comm. Math. Phys. 201 (1999), no. 2, 305–326. MR 1682230, DOI 10.1007/s002200050557
  • È. B. Vinberg, The theory of homogeneous convex cones, Trudy Moskov. Mat. Obšč. 12 (1963), 303–358 (Russian). MR 0158414
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Additional Information
  • D. Cooper
  • Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
  • MR Author ID: 239760
  • Email: cooper@math.ucsb.edu
  • D. D. Long
  • Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
  • MR Author ID: 201087
  • Email: long@math.ucsb.edu
  • Received by editor(s): July 18, 2013
  • Received by editor(s) in revised form: April 10, 2014, May 28, 2014, and June 24, 2014
  • Published electronically: April 1, 2015
  • Additional Notes: The first author was partially supported by NSF grants 1065939, 1045292, 1207068
    The second author was partially supported by NSF grants.
  • Communicated by: Daniel Ruberman
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 4561-4569
  • MSC (2010): Primary 57M05
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12579-8
  • MathSciNet review: 3373953