Contractible polyhedra in products of trees and absolute retracts in products of dendrites

Details Contractible polyhedra in products of trees and absolute retracts in products of dendrites Contractible polyhedra in products of trees and absolute retracts in products of dendrites

2011-02-03

arxiv.org/abs/1102.0696v6

Mathematics

Geometric Topology

18 pages

Scientific paper

We show that a compact n-polyhedron PL embeds in a product of n trees if and only if it collapses onto an (n-1)-polyhedron. If the n-polyhedron is contractible and n\ne 3 (or n=3 and the Andrews-Curtis Conjecture holds), the product of trees may be assumed to collapse onto the image of the embedding. In contrast, there exists a 2-dimensional compact absolute retract X such that X\times I^k does not embed in any product of 2+k dendrites for each k.

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