Higson–Kasparov–Trout introduced an infinite-dimensional Clifford algebra of a Hilbert space, and verified Bott periodicity on -theory. To develop an algebraic topology of maps between Hilbert spaces, in this paper we introduce an induced Hilbert Clifford algebra and construct an induced map between -theory of the Higson–Kasparov–Trout Clifford algebra and the induced Clifford algebra. We also compute its -group for some concrete case.
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Tsuyoshi Kato, Induced map on -theory for certain -equivariant maps between Hilbert spaces. J. Noncommut. Geom. 15 (2021), no. 4, pp. 1433–1467DOI 10.4171/JNCG/442