Taut sutured handlebodies as twisted homology products

TL;DR

This paper explores the relationship between the topology of taut sutured handlebodies and the complexity of representations needed to realize them as twisted homology products, providing insights into their structural properties.

Contribution

It offers new results linking the topology of taut sutured handlebodies with the complexity of the representations that realize them as homology products.

Findings

Established bounds on representation complexity

Connected topological features with algebraic realization complexity

Provided examples illustrating the relationship

Abstract

Friedl and Kim show any taut sutured manifold can be realized as a twisted homology product, but their proof gives no practical description of how complicated the realizing representation needs to be. We give a number of results illustrating the relationship between the topology of a taut sutured handlebody and the complexity of a representation realizing it as a homology product.