O. Musin

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math.AT2026

Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions

Oleg R. Musin

A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on $d$ that guarantee-for a given set of $m$ measures in $\…

math.AT2025

On essential simplicial maps $S^{3} \to S^{2}$

Mikhail V. Bludov, Sergei Vad. Fomin, Oleg R. Musin

A fiber-uniform bound on the complexity of an essential simplicial map $S^{3} \to S^{2}$ is proven, and the tightness of the bound is investigated. It follows that the triangula…

math.AT2025

Homotopy groups and quantitative Sperner-type lemma

Oleg R. Musin

We consider a generalization of Sperner's lemma for a triangulation $T$ of $(m + 1)$ -discs $D$ whose vertices are colored in $n + 2$ colors. A proper coloring of $T$ on the boundary of…

Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions

On essential simplicial maps S3→S2

Homotopy groups and quantitative Sperner-type lemma

On essential simplicial maps $S^{3} \to S^{2}$