On the K-theory of matroids with Tutte coverings

TL;DR

This paper computes the K-theory of the category of matroids using Tutte coverings, establishing an equivalence with graphic matroids on looped forests and relating it to $C_2$-spectra.

Contribution

It explicitly determines the K-theory of matroids with Tutte coverings and links it to graphic matroids and $C_2$-spectra, providing new algebraic insights.

Findings

K-theory of matroids is equivalent to that of graphic matroids on looped forests

The covering family generated by isomorphisms simplifies the K-theory computation

Establishes an equivalence of $C_2$-spectra for the categories involved

Abstract

The aim of this work is to explicitly compute the K-theory of the category of matroids with respect to the covering family of Tutte coverings. In particular, we show that this is equivalent to the K-theory spectrum of the category of graphic matroids on looped forests, with the covering family generated by isomorphisms. Further, we show that this yields an equivalence of $C_2$-spectra.