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Faithfulness Properties of the Burau Representation

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003528/00001

Material Information

Title: Faithfulness Properties of the Burau Representation
Physical Description: Book
Language: English
Creator: Hussey, Caleb
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2005
Publication Date: 2005

Subjects

Subjects / Keywords: Burau Representation
Braid Group/Faithful
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This paper is intended as a unified treatment of the existing results on the faithfulness of the Burau representation. Such a treatment is desirable because the articles cited often use conflicting conventions, sometimes even within a single paper. We present the results in terms of a single set of conventions, and we clarify or clean up proofs as needed. We introduce the n-strand braid group Bn as a set of homotopy classes of maps on Dn. We then define a covering space Dn of Dn and note that as we defined it, Bn acts naturally on the relative homology of Dn . We use this action to construct the Burau representation of Bn. Switching to a reduced form of the representation allows us to prove the Burau representation is faithful for n < 3. The representation is shown to be unfaithful for n > 5 by means of a curve in D5 with certain homological properties.
Statement of Responsibility: by Caleb Hussey
Thesis: Thesis (B.A.) -- New College of Florida, 2005
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. 2005 H9
System ID: NCFE003528:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003528/00001

Material Information

Title: Faithfulness Properties of the Burau Representation
Physical Description: Book
Language: English
Creator: Hussey, Caleb
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2005
Publication Date: 2005

Subjects

Subjects / Keywords: Burau Representation
Braid Group/Faithful
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This paper is intended as a unified treatment of the existing results on the faithfulness of the Burau representation. Such a treatment is desirable because the articles cited often use conflicting conventions, sometimes even within a single paper. We present the results in terms of a single set of conventions, and we clarify or clean up proofs as needed. We introduce the n-strand braid group Bn as a set of homotopy classes of maps on Dn. We then define a covering space Dn of Dn and note that as we defined it, Bn acts naturally on the relative homology of Dn . We use this action to construct the Burau representation of Bn. Switching to a reduced form of the representation allows us to prove the Burau representation is faithful for n < 3. The representation is shown to be unfaithful for n > 5 by means of a curve in D5 with certain homological properties.
Statement of Responsibility: by Caleb Hussey
Thesis: Thesis (B.A.) -- New College of Florida, 2005
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. 2005 H9
System ID: NCFE003528:00001

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