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Abstract A simple polytopePis calledB-rigidif its combinatorial type is determined by the cohomology ring of the moment-angle manifold$$\mathcal {Z}_P$$overP. 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 thatB-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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Matching Polytopes, Gorensteinness, and the Integer Decomposition Property
Abstract The matching polytope of a graphGis the convex hull of the indicator vectors of the matchings onG. We characterize the graphs whose associated matching polytopes are Gorenstein, and then prove that all Gorenstein matching polytopes possess the integer decomposition property. As a special case study, we examine the matching polytopes of wheel graphs and show that they arenotGorenstein, butdopossess the integer decomposition property.
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- Award ID(s):
- 2102921
- PAR ID:
- 10583111
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Graphs and Combinatorics
- Volume:
- 41
- Issue:
- 3
- ISSN:
- 0911-0119
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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