Geodesic
Product decompositions of moment-angle manifolds and B-rigidity
Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1313-1325

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DOI

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.
DOI : 10.4153/S0008439523000383
Mots-clés : Moment-angle complex, cohomological rigidity, Stanley–Reisner ring, quasitoric manifold 
Amelotte, Steven; Briggs, Benjamin. Product decompositions of moment-angle manifolds and B-rigidity. Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1313-1325. doi: 10.4153/S0008439523000383
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     title = {Product decompositions of moment-angle manifolds and {B-rigidity}},
     journal = {Canadian mathematical bulletin},
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     year = {2023},
     volume = {66},
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     doi = {10.4153/S0008439523000383},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000383/}
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