O. Musin

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math.AT2026

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

Oleg R. Musin

We prove a Borsuk--Ulam-type zero theorem for the Stiefel manifold $V_{n, k}$ equipped with a free action of the hyperoctahedral group $B_{k} = (Z /2)^{k} ⋊ S_{k}$ . The existen…

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.AT2023

A Second Homotopy Group for Digital Images

Gregory Lupton, Oleg Musin, Nicholas A. Scoville +2

We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second hom…

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

On essential simplicial maps S3→S2

A Second Homotopy Group for Digital Images

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