A pairing between super Lie-Rinehart and periodic cyclic homology
Maszczyk, Tomasz
arXiv, 0512040 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-12-01
Classification:  Mathematics - K-Theory and Homology,  Mathematical Physics,  Primary 16E40, 17B35, 19K56, Secondary 46L87 
@article{0512040,
     author = {Maszczyk, Tomasz},
     title = {A pairing between super Lie-Rinehart and periodic cyclic homology},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512040}
}

Maszczyk, Tomasz. A pairing between super Lie-Rinehart and periodic cyclic homology. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512040/