On the K-theory of matroids with Tutte coverings

2026/03/18 by Luigi Caputi, Sabino Di Trani · 1 voice
Mathematics · #math.KT #math.AT #math.CO

paper · pdf

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 C₂-spectra.

Citations

• Realizing the Tutte polynomial as a cut-and-paste K-theoretic invariant
• A categorification for the characteristic polynomial of matroids
• A trace map on higher scissors congruence groups
• A categorification for the signed chromatic polynomial
• A categorification for the Tutte polynomial
• Categorification of the Dichromatic Polynomial for Graphs
• CATEGORIFICATION OF THE DICHROMATIC POLYNOMIAL FOR GRAPHS
• A categorification for the chromatic polynomial

Discussions

• Luigi Caputi, Sabino Di Trani: On the K-theory of matroids with Tutte coverings https://arxiv.org/abs/2603.18288 https://arxiv.org/pdf/2603.18288 https://arxiv.org/html/2603.18288 [bsky, 0 points, 0 comments]

Related

• Realizing the Tutte polynomial as a cut-and-paste K-theoretic invariant
• K-theoretic Tutte polynomials of morphisms of matroids
• Flag matroids: algebra and geometry
• Matroid colorings of KKM covers
• The Tutte dichromate and Whitney homology of matroids