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Cyclic Covering Spaces of Knot Complements

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003919/00001

Material Information

Title: Cyclic Covering Spaces of Knot Complements
Physical Description: Book
Language: English
Creator: Flanagan, Mark
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2008
Publication Date: 2008

Subjects

Subjects / Keywords: Knots
Covering Spaces
Algebraic Topology
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Covering spaces comprise important classes of knot invariants. The purpose of this expository thesis is to provide an introduction to the study of classical knots that focuses on the construction of cyclic covering invariants. First we will introduce knots, with a discussion of knot equivalence and invariants. Then, after developing the necessary homotopy theory, we construct cyclic covering spaces of knot complements using Seifert surfaces. This allows us to define the Alexander polynomial of a knot � a powerful knot invariant. We conclude the thesis with a theorem that relates the Alexander polynomial to the order of the first homology of cyclic branched covers of the three-sphere.
Statement of Responsibility: by Mark Flanagan
Thesis: Thesis (B.A.) -- New College of Florida, 2008
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Mullins, David

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2008 F58
System ID: NCFE003919:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003919/00001

Material Information

Title: Cyclic Covering Spaces of Knot Complements
Physical Description: Book
Language: English
Creator: Flanagan, Mark
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2008
Publication Date: 2008

Subjects

Subjects / Keywords: Knots
Covering Spaces
Algebraic Topology
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Covering spaces comprise important classes of knot invariants. The purpose of this expository thesis is to provide an introduction to the study of classical knots that focuses on the construction of cyclic covering invariants. First we will introduce knots, with a discussion of knot equivalence and invariants. Then, after developing the necessary homotopy theory, we construct cyclic covering spaces of knot complements using Seifert surfaces. This allows us to define the Alexander polynomial of a knot � a powerful knot invariant. We conclude the thesis with a theorem that relates the Alexander polynomial to the order of the first homology of cyclic branched covers of the three-sphere.
Statement of Responsibility: by Mark Flanagan
Thesis: Thesis (B.A.) -- New College of Florida, 2008
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Mullins, David

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2008 F58
System ID: NCFE003919:00001

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