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Structure of $C_{pq}$-cohomology of points and slice tower

Surojit Ghosh

Abstract

The additive structure of the $RO(C_{pq})$-graded Bredon cohomology $S^0$ with coefficients in the constant Mackey functor was computed in \cite{BG19}. Using that computation, the ring structure in the positive degrees has been computed here. Further, we calculate the slices of the spectrum $S^V \wedge H\uZ$ for any representation $V.$

Structure of $C_{pq}$-cohomology of points and slice tower

Abstract

The additive structure of the -graded Bredon cohomology with coefficients in the constant Mackey functor was computed in \cite{BG19}. Using that computation, the ring structure in the positive degrees has been computed here. Further, we calculate the slices of the spectrum for any representation

Paper Structure

This paper contains 5 sections, 18 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Organization.
  3. preliminaries
  4. The ring structure
  5. $C_{pq}$-slices for the spectrum $S^V \wedge H \underline{\mathbb{Z}}$

Key Result

Theorem \oldthetheorem

In positive degree, the ring $\tilde{H}^{\bigstar}_{C_{pq}}(S^0)$ is isomorphic to where $a_V$ and $u_V$ are certain classes defined in au.

Theorems & Definitions (43)

  • Theorem \oldthetheorem
  • Theorem \oldthetheorem
  • Definition \oldthetheorem
  • Example \oldthetheorem
  • Proposition \oldthetheorem
  • proof
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Proposition \oldthetheorem
  • ...and 33 more