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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The 3-manifold recognition problem
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by Robert J. Daverman and Thomas L. Thickstun PDF
Trans. Amer. Math. Soc. 358 (2006), 5257-5270 Request permission

Abstract:

We introduce a natural Relative Simplicial Approximation Property for maps from a 2-cell to a generalized 3-manifold and prove that, modulo the Poincaré Conjecture, 3-manifolds are precisely the generalized 3-manifolds satisfying this approximation property. The central technical result establishes that every generalized 3-manifold with this Relative Simplicial Approximation Property is the cell-like image of some generalized 3-manifold having just a 0-dimensional set of nonmanifold singularities.
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Additional Information
  • Robert J. Daverman
  • Affiliation: Department of Mathematics, The University of Tennessee at Knoxville, Knoxville, Tennessee 37996-1300
  • Email: daverman@math.utk.edu
  • Thomas L. Thickstun
  • Affiliation: Department of Mathematics, Texas State University, San Marcos, Texas 78666
  • Email: tt04@txstate.edu
  • Received by editor(s): April 21, 2003
  • Received by editor(s) in revised form: July 21, 2004
  • Published electronically: December 20, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 5257-5270
  • MSC (2000): Primary 57N10, 57P99; Secondary 57M30, 57N60, 57N75
  • DOI: https://doi.org/10.1090/S0002-9947-05-03786-4
  • MathSciNet review: 2238915