University of Illinois Urbana-Champaign

The Structure of the Cayley Complex and a Cubic-Time Algorithm for Solving the Conjugacy Problem for Groups of Prime Alternating Knots

Johnsgard, Karin Luisa

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https://hdl.handle.net/2142/72539

Description

Title
The Structure of the Cayley Complex and a Cubic-Time Algorithm for Solving the Conjugacy Problem for Groups of Prime Alternating Knots
Author(s)
Johnsgard, Karin Luisa
Issue Date
1993
Doctoral Committee Chair(s)
Schupp, Paul E.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
  • This paper in Combinatorial Group Theory explores the geometric structure of the augmented group presentations of elementary alternating links, a structure which reflects the form of the link diagram in a simple and beautiful way. The extreme regularity of this tree-like structure is used to derive a quadratic-time algorithm for producing all geodesic representatives for any given group element, and for solving the Conjugacy Problem in cubic-time. Regular normal forms are also examined for this class of link groups, which includes (and completely distinguishes) all alternating prime knots. Possible extensions of this work are discussed.
  • This paper is as self-contained as possible, requiring only some familiarity with groups and with some concepts from first-year topology; some experience with graphs and/or geometric 2-complexes is helpful. The preface includes a history of knot theory and combinatorial group theory.
Graduation Semester
1993
Type of Resource
text
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http://hdl.handle.net/2142/72539

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