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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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DOI

10.1016/0378-1119(87)90138-7

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1432-0916

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Periodicity and the Determinant Bundle

Authors: Richard Melrose Frédéric Rochon
Publish Date: 2007/06/16
Volume: 274, Issue: 1, Pages: 141-186
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Abstract

The infinite matrix ‘Schwartz’ group G −∞ is a classifying group for odd Ktheory and carries Chern classes in each odd dimension generating the cohomology These classes are closely related to the Fredholm determinant on G −∞ We show that while the higher even Schwartz loop groups of G −∞ again classifying for odd Ktheory do not carry multiplicative determinants generating the first Chern class ‘dressed’ extensions corresponding to a star product do carry such functions We use these to discuss Bott periodicity for the determinant bundle and the eta invariant In so doing we relate two distinct extensions of the eta invariant to selfadjoint elliptic operators and to elliptic invertible suspended families and show that the corresponding τ invariant is a determinant in this sense

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  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
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  16. Phase Boundaries in Algebraic Conformal QFT
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