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The 3-manifold recognition problem
Authors:
Robert J. Daverman and Thomas L. Thickstun
Journal:
Trans. Amer. Math. Soc. 358 (2006), 5257-5270
MSC (2000):
Primary 57N10, 57P99; Secondary 57M30, 57N60, 57N75
Posted:
December 20, 2005
MathSciNet review:
2238915
Full-text PDF Free Access
Abstract |
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Additional Information
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
DOI:
http://dx.doi.org/10.1090/S0002-9947-05-03786-4
PII:
S 0002-9947(05)03786-4
Keywords:
Generalized 3-manifold,
resolvable,
simplicial approximation property,
relative simplicial approximation,
tame embedding,
locally $1$-coconnected
Received by editor(s):
April 21, 2003
Received by editor(s) in revised form:
July 21, 2004
Posted:
December 20, 2005
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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