Generalizations of Tucker–Fan–Shashkin Lemmas

Authors

Oleg R. Musin, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

6-16-2016

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.

Comments

Copyright © 2016, Institute for Mathematical Sciences (IMS), Stony Brook University, NY

Recommended Citation

Musin, O.R. Generalizations of Tucker–Fan–Shashkin Lemmas. Arnold Math J. 2, 299–308 (2016). https://doi.org/10.1007/s40598-016-0045-7

Publication Title

Arnold Math J.

DOI

10.1007/s40598-016-0045-7