Odd characteristic classes in entire cyclic homology and equivariant loop space homology

Sergio Cacciatori; Batu Güneysu

Odd characteristic classes in entire cyclic homology and equivariant loop space homology

K-Theory and Homology 2019-04-29 v2 Mathematical Physics Differential Geometry math.MP

Authors: Sergio Cacciatori , Batu Güneysu

Abstract

Given a compact manifold $M$ and $g\in C^{\infty}(M,U(l;\mathbb{C}))$ we construct a Chern character $\mathrm{Ch}^-(g)$ which lives in the odd part of the equivariant (entire) cyclic Chen-normalized bar complex $\underline{\mathscr{C}}(\Omega_{\mathbb{T}}(M\times \mathbb{T}))$ 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 $g\mapsto \mathrm{Ch}^-(g)$ induces a well-defined group homomorphism from the $K^{-1}$ theory of $M$ to the odd homology group of $\underline{\mathscr{C}}(\Omega_{\mathbb{T}}(M\times \mathbb{T}))$

Keywords

odd characteristic classes entire cyclic homology equivariant loop space chern character k-theory compact manifold

Cite

@article{arxiv.1805.07449,
  title  = {Odd characteristic classes in entire cyclic homology and equivariant loop space homology},
  author = {Sergio Cacciatori and Batu Güneysu},
  journal= {arXiv preprint arXiv:1805.07449},
  year   = {2019}
}

Comments

Growth conditions to the space of differential forms on loop space added; detailed calculations for the equivariant Chen integral map added;

Odd characteristic classes in entire cyclic homology and equivariant loop space homology

Abstract

Keywords

Cite

Comments

Related papers