On upper and lower bounds for finite group actions on bounded surfaces, handlebodies, closed handles and finite graphs

TL;DR

This survey reviews known bounds on finite group actions across various topological objects with free fundamental groups, including surfaces, handlebodies, and finite graphs, highlighting their similarities and differences.

Contribution

It compiles and compares existing results on bounds for finite group actions on these objects, emphasizing their common feature of free fundamental groups.

Findings

Summarizes bounds for finite group actions on surfaces and 3D handlebodies.

Highlights the role of free fundamental groups in these bounds.

Provides a unified perspective across different topological objects.

Abstract

This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all have free fundamental group).