首页|Odd characteristic classes in entire cyclic homology and equivariant loop space homology
Odd characteristic classes in entire cyclic homology and equivariant loop space homology
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Given a compact manifold M and a smooth map g: M -> U(l x l; C) fromM to the Lie group of unitary l x l matrices with entries in C, we construct a Chern character Ch(-)g/ which lives in the odd part of the equivariant (entire) cyclic Chen-normalized cyclic complex N-epsilon (Omega(T)(M x T)) of M, and which is mapped to the odd Bismut-Chern character under the equivariant Chen integral map. It is also shown that the assignment g ((bar right arrow)) Ch(-)g/ induces a well-defined group homomorphism from the K-1 theory of M to the odd homology group of N-epsilon (Omega(T)(M x T)).
Characteristic classesloop spacesequivariant homologycyclic homologyChen integralsBismut-Chern characterELLIPTIC FAMILIESCHERN CHARACTER
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