The group O of Bogoliubov automorphisms of the infinite dimensional Clifford algebra, implementable in a Fock representation, the analogous group of automorphisms of the canonical commutation relations and various generalisations are discussed. Their homotopy type is determined in a topology naturally defined by the spin and metaplectic representations. A theorem of Araki and Evans on a 2-index for certain projections is generalised using our "mod 2" index for ???. Connections with _K_1 of certain Banach algebras are described.
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Alan L. Carey, Some Infinite Dimensional Groups and Bundles. Publ. Res. Inst. Math. Sci. 20 (1984), no. 6, pp. 1103–1117DOI 10.2977/PRIMS/1195180373