Multiplicativity and nonrealizable equivariant chain complexes

DOI10.1016/J.JPAA.2022.107023zbMath1521.55003arXiv1905.03091MaRDI QIDQ6318407

Henrik Rüping, Marc Stephan

Publication date: 8 May 2019

Abstract: Let $G$ be a finite $p$-group and $mathbbF$ a field of characteristic $p$. We filter the cochain complex of a free $G$-space with coefficients in $mathbbF$ by powers of the augmentation ideal of $mathbbFG$. We show that the cup product induces a multiplicative structure on the arising spectral sequence and compute the $E_1$-page as a bigraded algebra. As an application, we prove that recent counterexamples of Iyengar and Walker to an algebraic version of Carlsson's conjecture can not be realized topologically.

Mathematics Subject Classification ID

Cohomology of groups (20J06) Finite groups of transformations in algebraic topology (including Smith theory) (55M35) Finite transformation groups (57S17) Homological conjectures (intersection theorems) in commutative ring theory (13D22) Spectral sequences in algebraic topology (55T99)

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