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arXiv · 2503.06267

Magnetic Equivariant K-theory

Higinio Serrano·Bernardo Uribe·Miguel A. Xicoténcatl
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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.

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Higinio Serrano, Bernardo Uribe, Miguel A. Xicoténcatl. 2025-03-08. Magnetic Equivariant K-theory. https://arxiv.org/abs/2503.06267

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