The Gauss-Manin connection and noncommutative tori

Abstract

We use Getzler's Gauss-Manin connection to prove the invariance of periodic cyclic cohomology for the smooth deformation of noncommutative tori. We explicitly calculate the parallel translation maps and use them to describe the behavior of the Chern-Connes pairing under this deformation.

References in corpus (2)

• On the Gauss-Manin connection in cyclic homology
• Monodromy of the Gauss-Manin connection for deformation by group cocycles

Cited by in corpus (1)

• Smooth crossed products of Rieffel's deformations