PreprintCC BY 4.0arXiv
New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres
Abstract
We prove that the moment-angle manifold 𝒵𝒦 is diffeomorphic to a connected sum of products of spheres when 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 𝒦 of odd dimension, we prove the diffeomorphism 𝒵𝒦 ≅ M1#⋯# Mk, where each Mi 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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BibTeX
@misc{kovyrshina2026families,
title = {{New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres}},
author = {Victoria Kovyrshina and Taras Panov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19945},
eprint = {2609.19945},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19945},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres
AU - Victoria Kovyrshina
AU - Taras Panov
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19945
UR - https://arxiv.org/abs/2609.19945
AB - We prove that the moment-angle manifold 𝒵_𝒦 is diffeomorphic to a connected sum of products of spheres when 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 𝒦 of odd dimension, we prove the diffeomorphism 𝒵_𝒦 ≅ M_1#⋯# 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.
ER -