A residue formula for the fundamental Hochschild class of the Podles sphere

TL;DR

This paper presents a residue formula expressing the fundamental Hochschild cohomology class of the standard Podles quantum sphere using its spectral triple, linking noncommutative geometry and quantum group theory.

Contribution

It provides a novel residue formula for the Hochschild class of the Podles sphere based on its spectral triple, advancing the understanding of noncommutative geometric invariants.

Findings

Residue formula for Hochschild class derived

Connection established between spectral triple and Hochschild cohomology

Enhances computational tools for quantum spheres

Abstract

The fundamental Hochschild cohomology class of the standard Podles quantum sphere is expressed in terms of the spectral triple of Dabrowski and Sitarz by means of a residue formula.