A Bott Periodicity Theorem for Infinite Dimensional Euclidean Space

Nigel Higson, Gennadi Kasparov, Jody Trout

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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-commutativeC*-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).

Original languageEnglish (US)
Pages (from-to)1-40
Number of pages40
JournalAdvances in Mathematics
Volume135
Issue number1
DOIs
Publication statusPublished - Apr 15 1998

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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