The Dehn-Nielsen-Baer Theorem for Bounded Surfaces

math.GT

/ Authors

/ Abstract

Let $Σ$ be a bounded surface. We prove the Dehn-Nielsen-Baer theorem for bounded surfaces to show that the mapping class group of $Σ$ is isomorphic to the automorphisms of the fundamental groupoid of $Σ$ that fix loops around the boundary.

The Dehn-Nielsen-Baer Theorem for Bounded Surfaces

math.GT

/ Authors

Elysia Wang

/ Abstract

Let $Σ$ be a bounded surface. We prove the Dehn-Nielsen-Baer theorem for bounded surfaces to show that the mapping class group of $Σ$ is isomorphic to the automorphisms of the fundamental groupoid of $Σ$ that fix loops around the boundary.