Title

Fantastic Topological Surfaces And How To Classify Them

Date

5-31-2018 1:00 PM

End Time

31-5-2018 1:20 PM

Location

HWC 204

Session Chair

Cheryl Beaver

Session Chair

Leanne Merrill

Session Title

Mathematics Capstone Project Presentations

Presentation Type

Presentation

Faculty Sponsor(s)

Leanne Merrill

Abstract

The Classification theorem of Compact Surfaces shows us that all nonempty, compact connected 2-dimensional manifolds are homeomorphic to one of three categories of manifolds. These cases consist of the sphere, the connected sum of g-holed tori, or a connected sum of projective planes. We aim to rigorously prove the theorem via verification of the requisite auxiliary theorems and lemmas. This will require an analysis of a relationship that can be established between these topological surfaces and equivalent representational polygons. Then, a set of elementary transformations will be used to reduce all possible polygonal presentations of surfaces to one of the three nonequivalent cases.

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May 31st, 1:00 PM May 31st, 1:20 PM

Fantastic Topological Surfaces And How To Classify Them

HWC 204

The Classification theorem of Compact Surfaces shows us that all nonempty, compact connected 2-dimensional manifolds are homeomorphic to one of three categories of manifolds. These cases consist of the sphere, the connected sum of g-holed tori, or a connected sum of projective planes. We aim to rigorously prove the theorem via verification of the requisite auxiliary theorems and lemmas. This will require an analysis of a relationship that can be established between these topological surfaces and equivalent representational polygons. Then, a set of elementary transformations will be used to reduce all possible polygonal presentations of surfaces to one of the three nonequivalent cases.