Weakly framed surface configurations, Heisenberg homology and Mapping Class Group action

TL;DR

This paper introduces new representations of the mapping class group of punctured surfaces using Heisenberg homology actions on circle bundles, linking surface configurations with algebraic structures.

Contribution

It presents a novel approach to constructing mapping class group representations via Heisenberg homology, connecting surface topology with algebraic and geometric structures.

Findings

Constructed new representations of the mapping class group.

Linked surface configurations with Heisenberg homology.

Provided insights into the algebraic structure of surface mapping classes.

Abstract

We obtain representations of the f-based Mapping Class Group of oriented punctured surfaces from an action of mapping classes on Heisenberg homologies of a circle bundle over surface configurations.