Abstract:
For a commutative ring ${\mathbb k}$ with unit, we describe and study various differential graded ${\mathbb k}$-modules and ${\mathbb k}$-algebras as models for the cohomology of polyhedral products $(\underline{CX},\underline X)^K$. Along the way, we prove that the integral cohomology $H^*((D^1, S^0)^K; \mathbb{Z})$ of the real moment-angle complex is a Tor module, one that does not come from a geometric setting. As an application, this work sets the stage for studying the based loop space of $\Sigma (\underline{CX}, \underline X)^K$.
Keywords:polyhedral products, moment angle complexes, cohomological models.
Citation:
M. Bendersky, J. Grbić, “Models for the Cohomology of Certain Polyhedral Products”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 43–57
\Bibitem{BenGrb24}
\by M.~Bendersky, J.~Grbi{\'c}
\paper Models for the Cohomology of Certain Polyhedral Products
\inbook Topology, Geometry, Combinatorics, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 326
\pages 43--57
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4417}
\crossref{https://doi.org/10.4213/tm4417}
Citation in format AMSBIB
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