Some Infinite Dimensional Groups and Bundles

Abstract

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.