| Authors: | Nigel Higson, Gennadi Kasparov and Jody Trout |
| Title: | A Bott periodicity theorem for infinite dimensional Hilbert space |
| Publication Information: | Advances in Math., 135 (1999), 1-40 |
| Abstract: | We formulate and prove an equivariant Bott periodicity theorem for infinite dimensional Euclidean vector spaces. The main features of our argument are (i) the construction of a non-commutative C*-algebra to play the role of the algebra of functions on infinite dimensional Euclidean space; and (ii) the construction of a certain index one elliptic partial differential operator which provides the basis for an inverse to the Bott periodicity map. These tools have applica- tions to index theory and the Novikov conjecture, notably a proof of the Novikov conjecture for amenable groups (the applications will be considered elsewhere). |