Generalizations of Tucker-Fan-Shashkin lemmas
Combinatorics
2016-10-07 v5 Geometric Topology
Abstract
Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about the doubling of manifolds with boundaries that are BUT-manifolds.
Keywords
Cite
@article{arxiv.1409.8637,
title = {Generalizations of Tucker-Fan-Shashkin lemmas},
author = {Oleg R. Musin},
journal= {arXiv preprint arXiv:1409.8637},
year = {2016}
}
Comments
10 pages, 2 figures