Development of the Alexander Polynomial of Single Component Knots via Siefert Surfaces
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Authors
Pike, Timothy Martin
Issue Date
1997
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
This document explains the development of the Alexander Polynomial via Seifert Surfaces. To accomplish
this, a few topics are considered. As a pseudo Table of Contents, here is a list of what's included.
I. Preliminaries and Definitions
II. Construction of Seifert Surfaces
Ill. Construction of the Seifert Graph
IV. Euler Characteristic and Genus of surfaces
V. Homeomorphism between the sphere and the projective plane
VI. The Fundamental Group of a Seifert Surface
VII. The Seirert Matrix and S-Equivalence of Matrices
VIII. The invariance of the Alexander Polynomial.
IX. Appendix: A few "cheats" on computing the linking numbers for the Seifert Matrix
Description
iii, 14 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.