Stable cohomology of alternating groups
Fedor Bogomolov, Christian B\"ohning
TL;DR
This paper computes the stable cohomology groups of alternating groups A_n with coefficients in Z/p for all n, i, and primes p, providing a comprehensive understanding of their cohomological structure.
Contribution
It determines the stable cohomology groups of alternating groups for all n, i, and primes p, a complete classification not previously available.
Findings
Explicit formulas for stable cohomology groups H^i_s (A_n, Z/p)
Results hold for all integers n, i, and primes p
Advances understanding of the algebraic topology of symmetric groups
Abstract
In this article we determine the stable cohomology groups H^i_s (A_n, Z/p) of the alternating groups A_n for all integers n and i, and all primes p.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models