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Freed-Moore K-theory

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arxiv 1705.09134 v4 pith:NYZVM6VZ submitted 2017-05-25 math.KT

Kiyonori Gomi This is my paper
classification math.KT
keywords k-theoryequivariantfredholmtwistedatiyahbasicbottclarifying
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The twisted equivariant K-theory given by Freed and Moore is a K-theory which unifies twisted equivariant complex K-theory, Atiyah's `Real' K-theory, and their variants. In a general setting, we formulate this K-theory by using Fredholm operators, and establish basic properties such as the Bott periodicity and the Thom isomorphism. We also provide formulations of the K-theory based on Karoubi's gradations in both infinite and finite dimensions, clarifying their relationship with the Fredholm formulation.

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  1. Free phases of Majorana fermions: Tenfold ways compared

    math-ph 2025-07 conditional novelty 6.0 of 10

    Neutral free fermion SPT phases protected by a real Z2-graded C*-algebra A are classified by the real K-theory group K_2(A^op), unifying charged and neutral tenfold-way classifications via Morita equivalence.

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