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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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On CE-resolving of 2-polyhedra up to the special polyhedra
by
Konstantin Salikhov
Coauthors: D. Repovs

A CE-resolvent (in PL-category) of a polyhedron P is a pair (Q, f) of a polyhedron Q and an onto map f : Q --> P having collapsible point-inverses. The stuidies of CE-resolvent begun by Edwards' Resolution Theorem. A 2-polyhedron is called special if

  1. every link of its points is either a circle or a \Theta-graph or a 1-skeleton of a 3-simplex;

  2. each connected component of P - P' and of P'- P'' is an open 2-disk and 1-disk, respectively.
For a 2-polyhedron P we denote by P' its intrinsic 1-skeleton and by P'' the intrinsic 0-skeleton of P'.

The studies of special 2-polyhedra begun by Casler's theorem on special 2-skeletons of 3-manifolds. We prove that every 2-polyhedron satisfying to 2) (plus some minor technical restriction) is CE-resolvable up to special one. Among the corollaries is the existence of a special 2-polyhedron, non-embeddable into R4.

Date received: June 25, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-38.