A Pairing Between Super Lie-Rinehart and Periodic Cyclic Homology |
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Authors: | Tomasz Maszczyk |
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Institution: | (1) Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00–956, Warszawa, Poland;(2) Institute of Mathematics, University of Warsaw, Banacha 2, 02–097, Warszawa, Poland |
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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.
The author was partially supported by the KBN grant 1P03A 036 26. |
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