2018/05/18 by Sergio Cacciatori, Cacciatori, Sergio, Batu Güneysu +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #math-ph #math.DG #math.KT #math.MP
paper · pdf · doi:10.48550/arxiv.1805.07449
Growth conditions to the space of differential forms on loop space added; detailed calculations for the equivariant Chen integral map added;
arxiv created 2019/04/25 · arxiv updated 2019/04/29
Given a compact manifold M and g∈ C∞(M,U(l;ℂ)) we construct a Chern character Ch-(g) which lives in the odd part of the equivariant (entire) cyclic Chen-normalized bar complex \underline\mathscrC(Ω_\mathbbT(M× \mathbbT)) 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↦ Ch-(g) induces a well-defined group homomorphism from the K-1 theory of M to the odd homology group of \underline\mathscrC(Ω_\mathbbT(M× \mathbbT))