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arXiv · 2211.05279

Borsuk-Ulam property for graphs

Daciberg Lima Gonçalves·Jesús González
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Abstract

For finite connected graphs $\Gamma$ and $G$, with $\Gamma$ admitting a free involution $\tau$, we characterize the based homotopy classes $\alpha\in[\Gamma,G]$ for which the Borsuk-Ulam property holds in the sense of Gon\c{c}alves, Guaschi and Casteluber-Laass, i.e., the homotopy classes $\alpha$ so that each of its representatives $f\in\alpha$ satisfies $f(x) = f(\tau\cdot x)$ for some $x\in\Gamma$. This is attained through a graph-braid-group perspective aided by the use of discrete Morse theory.

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Daciberg Lima Gonçalves, Jesús González. 2022-11-10. Borsuk-Ulam property for graphs. https://arxiv.org/abs/2211.05279

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