Geodesic
Models for the Cohomology of Certain Polyhedral Products
Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 43-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a commutative ring $\Bbbk $ with unit, we describe and study various differential graded $\Bbbk $-modules and $\Bbbk $-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, cohomological models.
Mots-clés : moment–angle complexes 
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M. Bendersky; J. Grbić. Models for the Cohomology of Certain Polyhedral Products. Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 43-57. http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a3/

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