## 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.## References

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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