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

## TL;DR

This paper provides an algebraic formula for p-completion of stable maps between classifying spaces, utilizing fusion data and Burnside modules, inspired by the Segal conjecture.

## Contribution

It introduces a novel algebraic approach to p-completion of stable maps based on fusion data and Burnside modules, extending the Segal conjecture.

## Key findings

- Derived an explicit algebraic formula for p-completion
- Connected fusion data with stable maps and Burnside modules
- Enhanced understanding of classifying space maps in algebraic terms

## 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.