An introduction to knots and knot groups

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Gwendolyn Eva Supulski (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
E. E. Posey

Abstract: The purpose of this paper is to present an introduction to the theory of knots and knot groups assuming an intermediate knowledge of group theory and topology on the part of the reader. Thus Chapter I is concerned with knots, equivalent knots, and tame knots. The basic definitions are given to develop the concept of a fundamental group for a topological space. The trivial knot is defined. Chapter II defines knot group and calculates the knot group for the trefoil, figure eight and square knots. The chapter ends with a proof of the existence of nontrivial knots. Chapter III presents two sophisticated methods of calculating knot groups of compound knots. Examples are given to illustrate the process. The development of knots and the fundamental group in Chapter I is based on material from Crowell and Fox [1J. Chapter II is based primarily on material from Crowell and Fox [1] and Fox [2]. The material on tori sequences and 2-sphere sequences in Chapter III is based heavily on a paper by E. E. Posey [4]. The remainder of the chapter, devoted to the van Kampen Theorem is based on material from Crowell and Fox [1]. The books of Hall [3] and Rotman [5] are recommended as references on group theory. For additional information on homotopy theory consult the book by Whitehead [6].

Additional Information

Language: English
Date: 1970
Knot theory

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