Generalizations of Shashkin and Tucker's lemma

Oleg R. Musin

Published 2014-09-30Version 1

Tucker's lemma is a combinatorial analog of the Borsuk--Ulam theorem (BUT). In 1996 Yu. A. Shashkin proved 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 the lemma about the doubling of manifolds with boundaries that are BUT--manifolds.