Triangulation of Surfaces and the Jordan Curve Theorem: A Graph Theoretic Approach

Sahu, Shrusti (2022) Triangulation of Surfaces and the Jordan Curve Theorem: A Graph Theoretic Approach. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Shrusti Sahu (17MS162)) 17MS162_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

The topic of this paper is about Triangulation of Surfaces. We will be looking through various proofs in the literature of this topic and try to expand on known ideas so that we can gain a better understanding and appreciation for this topic. We begin by studying some basic aspects of surfaces and triangulations. Then we go on to understand the Jordan curve theorem but with a graph theoretic approach and then finally we can prove the classic result that any compact surface is triangulable using the aforementioned theorem. We will further go on to look at a few applications of this result like the classification theorem for surfaces.

Actions (login required)

View Item