An Operator model for connective K-theory with reality

TL;DR

This paper constructs an explicit $ ext{C}_2$-equivariant model for the connective cover of real K-theory spectrum, providing a concrete framework for further mathematical exploration.

Contribution

It introduces a new explicit $ ext{C}_2$-equivariant symmetric ring spectrum model for the connective real K-theory spectrum, aligning with Dugger's model.

Findings

Explicit $ ext{C}_2$-equivariant model constructed

Model identified with Dugger's spectrum

Provides a concrete framework for connective real K-theory

Abstract

We construct an explicit model for the connective cover of the spectrum of $K$-theory with reality. This model is a $\ztwo$-equivariant commutative symmetric ring spectrum which identifies with another one due to D. Dugger.