Product decompositions of moment-angle manifolds and B-rigidity

2022/04/30 by Steven Amelotte, Amelotte, Steven, Benjamin Briggs +1
Mathematics · #13F55 #55U10 #57S12 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2205.00337

openalex publication_date 2022/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A simple polytope P is called B-rigid if its combinatorial type is determined by the cohomology ring of the moment-angle manifold Z_P over P. We show that any tensor product decomposition of this cohomology ring is geometrically realized by a product decomposition of the moment-angle manifold up to equivariant diffeomorphism. As an application, we find that B-rigid polytopes are closed under products, generalizing some recent results in the toric topology literature. Algebraically, our proof establishes that the Koszul homology of a Gorenstein Stanley-Reisner ring admits a nontrivial tensor product decomposition if and only if the underlying simplicial complex decomposes as a join of full subcomplexes.

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