A pairing between super Lie-Rinehart and periodic cyclic homology
Abstract
We consider a pairing producing various cyclic Hochschild cocycles, which led Alain Connes to cyclic cohomology. We are interested in geometrical meaning and homological properties of this pairing. We define a non-trivial pairing between the homology of a Lie-Rinehart (super-)algebra with coefficients in some partial traces and relative periodic cyclic homology. This pairing generalizes the index formula for summable Fredholm modules, the Connes-Kubo formula for the Hall conductivity and the formula computing the K0-group of a smooth noncommutative torus. It also produces new homological invariants of proper maps contracting each orbit contained in a closed invariant subset in a manifold acted on smoothly by a connected Lie group. Finally we compare it with the characteristic map for the Hopf-cyclic cohomology.
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Cite
@article{arxiv.math/0512040,
title = {A pairing between super Lie-Rinehart and periodic cyclic homology},
author = {Tomasz Maszczyk},
journal= {arXiv preprint arXiv:math/0512040},
year = {2009}
}
Comments
11 pages