Simplicial inverse sequences in extension theory
Geometric Topology
2017-03-14 v1 Algebraic Topology
General Topology
Abstract
In extension theory, in particular in dimension theory, it is frequently useful to represent a given compact metrizable space X as the limit of an inverse sequence of compact polyhedra. We are going to show that, for the purposes of extension theory, it is possible to replace such an X by a better metrizable compactum Z. This Z will come as the limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps that factor in a certain way. There will be a cell-like map from Z to X, and we shall show that if K is a CW-complex which is an absolute extensor for X, then K is also an absolute extensor for Z.
Cite
@article{arxiv.1703.04339,
title = {Simplicial inverse sequences in extension theory},
author = {Leonard R. Rubin and Vera Tonić},
journal= {arXiv preprint arXiv:1703.04339},
year = {2017}
}
Comments
17 pages