Murray State Theses and Dissertations

Abstract

Among topological spaces, manifolds draw a lot of interest. An
n-manifold is a space that is locally like R^n. Manifolds of dimension 2
are called surfaces. Using handle decomposition, we decompose surfaces
into k-handles, where 0< =k< =2. Techniques such as handle sliding and
handle cancellation allow us to get a more favorable representation of
our surface. We use these tools and calculation of the fundamental group
to classify all compact surfaces.

Year manuscript completed

2026

Year degree awarded

2026

Author's Keywords

topology, manifolds, surfaces, handle decomposition, algebraic topology

Degree Awarded

Master of Arts

Department

Mathematics & Statistics

College/School

Jesse D. Jones College of Science, Engineering and Technology

Thesis Advisor

Dubravko Ivansic

Committee Member

Ted Porter

Committee Member

Kelly Pearson

Document Type

Thesis

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