Title

The higher twisted index theorem for foliations

Document Type

Article

Publication Date

3-30-2017

Publication Title

Journal of Functional Analysis

ISSN

0022-1236

Volume

273

Issue

2

DOI

http://dx.doi.org/10.1016/j.jfa.2017.03.009

Abstract

Given a gerbe $L$, on the holonomy groupoid $\mathcal G$ of the foliation $(M, \mathcal F)$, whose pull-back to $M$ is torsion, we construct a Connes $\Phi$-map from the twisted Dupont-Sullivan bicomplex of $\mathcal G$ to the cyclic complex of the $L$-projective leafwise smoothing operators on $(M, \mathcal F)$. Our construction allows to couple the $K$-theory analytic indices of $L$-projective leafwise elliptic operators with the twisted cohomology of $B\mathcal G$ producing scalar higher invariants. Finally by adapting the Bismut-Quillen superconnection approach, we compute these higher twisted indices as integrals over the ambiant manifold of the expected twisted characteristic classes.

Comments

This is a post-print copy of "The higher twisted index theorem for foliations" published in the Journal of Functional Analysis.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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