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ArticleOriginal scientific text

Title

Cell-like resolutions of polyhedra by special ones

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001
  2. Department of Mathematics, Kolmogorov College, Kremenchugskaya, 11, Moscow, Russia 121357

Abstract

Suppose that P is a finite 2-polyhedron. We prove that there exists a PL surjective map f:Q → P from a fake surface Q with preimages of f either points or arcs or 2-disks. This yields a reduction of the Whitehead asphericity conjecture (which asserts that every subpolyhedron of an aspherical 2-polyhedron is also aspherical) to the case of fake surfaces. Moreover, if the set of points of P having a neighbourhood homeomorphic to the 2-disk is a disjoint union of open 2-disks, and every point of P has an arbitrarily small 2-dimensional neighbourhood, then we may additionally conclude that Q is a special 2-polyhedron.

Keywords

ENG
banana and pineapple trick, cell-like resolution, Whitehead conjecture, special polyhedron, fake surface

Bibliography

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Colloquium Mathematicum
2000/86/2
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Pages:
231-237
Main language of publication
English
Received
1999-12-06
Accepted
2000-01-21
Published
2000
Exact and natural sciences