arXiv subjects

Victoria Kovyrshina

Publications and source records attributed to Victoria Kovyrshina.

2 recordsLinked to original sources

arXiv2026

New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres

We prove that the moment-angle manifold $\mathcal Z_{\mathcal K}$ is diffeomorphic to a connected sum of products of spheres when $\mathcal K$ is a starshaped (in particular, polytopal) 3-dimensional simplicial sphere with exactly two missing edges that are not adjacent to each other. One of the summands of the connected sum is a product of three spheres. For neighbourly starshaped simplicial spheres $\mathcal K$ of odd dimension, we prove the diffeomorphism $\mathcal Z_{\mathcal K} \cong M_1\#\cdots\# M_k$, where each $M_i$ is a product of two spheres. We give an explicit description of the moment-angle manifolds corresponding to non-polytopal Barnette and Brückner spheres.

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arXiv2026

Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres

We prove that the moment-angle complex $\mathcal Z_K$ corresponding to a 3-dimensional simplicial sphere $K$ has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) $K$ is the boundary of a 4-dimensional cross-polytope, or (b) the one-skeleton of $K$ is a chordal graph, or (c) there are only two missing edges in $K$ and they form a chordless 4-cycle. For simplicial spheres $K$ of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism $H^*(\mathcal Z_K)\cong H^*(M)$ where $M$ is a connected sum of products of spheres.

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