Monodromy of the Gauss-Manin connection for deformation by group cocycles

TL;DR

This paper investigates how group cocycle deformations affect the Gauss-Manin connection's monodromy in algebraic structures, linking cyclic cohomology actions to group cohomology.

Contribution

It establishes a cohomological equivalence between Maurer-Cartan form action and cup product action in the context of algebra deformations by group cocycles.

Findings

Monodromy of Gauss-Manin connection computed explicitly for deformed algebras.

Maurer-Cartan form action is cohomologous to cup product action of group cocycle.

Provides a method to analyze deformation effects on cyclic cohomology.

Abstract

We consider the 2-cocycle deformation of algebras graded by discrete groups. The action of the Maurer-Cartan form on cyclic cohomology is shown to be cohomologous to the cup product action of the group cocycle. This allows us to compute the monodromy of the Gauss-Manin connection in the strict deformation setting.