On the K-Ring of the Classifying Space of the Dihedral Group

TL;DR

This paper explicitly describes the K-ring of the classifying space of the dihedral group, linking it to KO-ring polynomials of lens spaces and the Atiyah-Hirzebruch spectral sequence.

Contribution

It provides a detailed presentation of the K-ring with generators and relations, highlighting connections with KO-rings and spectral sequence filtrations.

Findings

Explicit generators and relations for the K-ring of the dihedral group's classifying space.

Connection established between K-ring generators and KO-ring polynomials of lens spaces.

Demonstration of generators within the Atiyah-Hirzebruch spectral sequence filtrations.

Abstract

We describe the K-ring of the classifying space of the dihedral group in terms of generators and the minimal set of relations by emphasising the connection with the polynomials arising in the KO-rings of lens spaces and demonstrating the generators of the filtrations of the Atiyah-Hirzebruch Spectral Squence.