Ossa's Theorem via the Kunneth formula

TL;DR

This paper computes the connective K-theory of the smash product of classifying spaces for cyclic groups using the K"unneth formula, providing explicit calculations for both unitary and orthogonal cases.

Contribution

It introduces a method to calculate connective K-theory of specific spaces via the K"unneth formula, extending known results to new cases.

Findings

Calculated connective unitary K-theory for cyclic group classifying spaces.

Derived connective orthogonal K-theory for the cyclic group of order two.

Established a K"unneth formula-based approach for these computations.

Abstract

Let $p$ be a prime. We calculate the connective unitary K-theory of the smash product of two copies of the classifying space for the cyclic group of order $p$, using a K\"{u}nneth formula short exact sequence. As a corollary, using the Bott exact sequence and the mod $2$ Hurewicz homomorphism we calculate the connective orthogonal K-theory of the smash product of two copies of the classifying space for the cyclic group of order two.