A formula for p-completion by way of the Segal conjecture

2017/04/02 by Sune Precht Reeh, Reeh, Sune Precht, Tomer M. Schlank +3
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1704.00271

Abstract

The Segal conjecture describes stable maps between classifying spaces in terms of (virtual) bisets for the finite groups in question. Along these lines, we give an algebraic formula for the p-completion functor applied to stable maps between classifying spaces purely in terms of fusion data and Burnside modules.

Related

• Unstable p-completion in motivic homotopy theory
• The Segal conjecture for smash powers
• Alternative stable homotopy classification of p-completed classifying spaces
• Assigning a classifying space to a fusion system up to F-isomorphism
• A remark on the group-completion theorem