English

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