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Differential $KO$-theory via gradations and mass terms

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arxiv 2111.01377 v2 pith:Z5B6NFUJ submitted 2021-11-02 math.KT cond-mat.str-elhep-thmath-phmath.ATmath.MP

Kiyonori Gomi , Mayuko Yamashita This is my paper
classification math.KTcond-mat.str-elhep-thmath-phmath.ATmath.MP
keywords theorydifferentialtermscliffordformalismgradationsmassmodels
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abstract

We construct models of the differential $KO$-theory and the twisted differential $KO$-theory, by refining Karoubi's $KO$-theory [Kar78] in terms of gradations on Clifford modules. In order for this, we set up the generalized Clifford superconnection formalism which generalizes the Quillen's superconnection formalism [Qui85]. One of our models can be regarded as classifying "fermionic mass terms" in physics.

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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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