Date of Award
5-2020
Document Type
Senior Thesis - Open Access
Abstract
This thesis presents the classification theorem of compact connected surfaces, its proof, and a computer implementation. The theorem, first stated by Mobius in 1861 and more formally by Jordan in 1866, states that every compact, connected surface is homeomorphic to either a 2-sphere, a connected sum of tori, or a connected sum of projective planes. The proof we present consists of an algorithm to take a polygon representation to normal form. A polygon representation of a surface is essentially the result of cutting the surface up until it lies flat, where we identify the cut edges such that we could paste it back together again. A polygon representation in normal form has distinguishable tori or projective plane components and can be easily classified from this state. The computer implementation is written in JavaScript and includes a graphical interface that allows the user to progress through the algorithm by cut and paste operations. The program is intended as a learning tool for students in introductory topology courses.
Recommended Citation
Dennis, Sarah, "A Program For Surface Classification" (2020). Senior Theses. 5.
https://digitalcommons.slc.edu/senior_theses/5