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Product decompositions of moment-angle manifolds and B-rigidity
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- Journal:
- Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023
- Published online by Cambridge University Press:
- 15 May 2023, pp. 1313-1325
- Print publication:
- December 2023
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A simple polytope P is called B-rigid if its combinatorial type is determined by the cohomology ring of the moment-angle manifold
$\mathcal {Z}_P$ 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.
Strong cohomological rigidity of toric varieties
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 5 / October 2017
- Published online by Cambridge University Press:
- 25 September 2017, pp. 971-992
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- October 2017
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