Magnetic Equivariant K-theory
K-Theory and Homology
2025-05-09 v3
Abstract
We present the fundamental properties of the K-theory groups of complex vector bundles endowed with actions of magnetic groups. In this work we show that the magnetic equivariant K-theory groups define an equivariant cohomology theory, we determine its coefficients, we show Bott's, Thom's and the degree shift isomorphism, we present the Atiyah-Hirzeburh spectral sequence, and we explicitly calculate two magnetic equivariant K-theory groups in order to showcase its applicability. These magnetic equivariant K-theory groups are relevant in condensed matter physics since they provide topological invariants of gapped Hamiltonians in magnetic crystals.
Cite
@article{arxiv.2503.06267,
title = {Magnetic Equivariant K-theory},
author = {Higinio Serrano and Bernardo Uribe and Miguel A. Xicoténcatl},
journal= {arXiv preprint arXiv:2503.06267},
year = {2025}
}
Comments
73 pages. Proposition 3.3 was corrected and references were added