# Generalized Chillingworth Classes on Subsurface Torelli Groups

## TL;DR

This paper provides a combinatorial description of the Chillingworth class for subsurface Torelli groups, establishing its naturality, uniqueness, and relation to the partitioned Johnson homomorphism.

## Contribution

It introduces a new combinatorial framework for understanding Chillingworth classes in subsurface Torelli groups and explores their fundamental properties and connections.

## Key findings

- Derived a combinatorial description of the Chillingworth class
- Proved naturality and uniqueness of the associated map
- Connected the Chillingworth class to the partitioned Johnson homomorphism

## Abstract

The contraction of the image of the Johnson homomorphism is called the Chillingworth class. In this paper, we derive a combinatorial description of the Chillingworth class for Putman's subsurface Torelli groups. We also prove the naturality and uniqueness properties of the map whose image is the dual of the Chillingworth classes of the subsurface Torelli groups. Moreover, we relate the Chillingworth class of the subsurface Torelli group to the partitioned Johnson homomorphism.