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Hilbert Grassmannians as classifying spaces

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arxiv 2503.20051 v2 pith:LRFTHAYI submitted 2025-03-25 math-ph math.MP

Giuseppe De Nittis , Kiyonori Gomi , Santiago G. Rendel This is my paper · ORCID
classification math-phmath.MP
keywords grassmannianshilbertspacesclassifyingapplicationclassescomputingendowed
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abstract

In this short work we prove that the Hilbert Grassmannians endowed with the weak topology are models for the classifying spaces of the unitary groups. As application of this result one can use Hilbert Grassmannians for the presentation of the $K$-theory of topological spaces by computing equivalences classes of homotopy equivalent maps.

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  1. A scheme for topological phases of the Weyl $C^*$-algebra

    math-ph 2026-07 unverdicted novelty 7.0 of 10

    Homotopy classes of sections of pure-state bundles of the Weyl C*-algebra recover the K-theoretic classification of type-A and AI topological insulators.

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