Triangulation and Classification of 2-Manifolds
Kushal Lalwani
TL;DR
This dissertation rigorously studies the topology and classification of 2-manifolds, providing detailed proofs and analyzing foundational work by Moise, Ahlfors, and Richards.
Contribution
It offers a comprehensive, detailed proof of the classification theorem for surfaces, including technical tools and analysis of prior foundational work.
Findings
Rigorous proof of the classification theorem for 2-manifolds
Analysis of foundational work by Moise, Ahlfors, and Richards
Development of technical tools for topological classification
Abstract
This dissertation contains a comprehensive study of the topology of 2-manifolds and a complementary analysis of the work done by Edwin E. Moise, L. V. Ahlfors and Ian Richards. Our aim is to study the well known classification of surfaces. Here we present the technical tools needed for proving rigorously the classification theorem and give a detailed proof using these tools.
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Taxonomy
TopicsDigital Image Processing Techniques · Computational Geometry and Mesh Generation · Homotopy and Cohomology in Algebraic Topology