School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Generalizations of Tucker–Fan–Shashkin Lemmas
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.
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
Arnold Math J.
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