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A Bott Periodicity Theorem for Infinite Dimensional Euclidean Space

✍ Scribed by Nigel Higson; Gennadi Kasparov; Jody Trout

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
450 KB
Volume
135
Category
Article
ISSN
0001-8708

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✦ Synopsis

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 applications to index theory and the Novikov conjecture, notably a proof of the Novikov conjecture for amenable groups (the applications will be considered elsewhere).

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