Mapping class groups of manifolds with boundary are of finite type

TL;DR

This paper proves that the mapping class group of a compact topological manifold with boundary is of finite type, given certain conditions on its dimension and connectivity, contributing to understanding its algebraic structure.

Contribution

It establishes the finite type property of mapping class groups for manifolds with boundary under specific dimensional and connectivity assumptions.

Findings

Mapping class groups are of finite type under certain conditions.

The result applies to compact topological manifolds with boundary.

Provides new insights into the algebraic structure of these groups.

Abstract

In this note we prove that the mapping class group of a compact topological manifold $M$ with boundary is of finite type, under assumptions on its dimension and connectivity.