The splitting of cohomology of p-groups with rank 2

TL;DR

This paper investigates the decomposition of the cohomology and Chow ring of p-completed classifying spaces of p-groups with rank 2, using stable homotopy splitting techniques for odd primes.

Contribution

It introduces a method to analyze the even-dimensional cohomology and Chow ring decompositions of BP for p-rank 2 p-groups via stable homotopy splitting.

Findings

Decomposition of even-dimensional cohomology of BP

Analysis of Chow ring structure for BP

Application of stable homotopy splitting for p-rank 2 groups

Abstract

Let BP be the p-completed classifying space of a p-group P with p-rank 2. For an odd prime p, by using stable homotopy splitting of BP, we study the decomposition of even dimensional parts of the integral cohomology and the Chow ring of BP.