- Bib ID:
- 3284042
- Format:
- Book and Microform
- Author:
- Bigelow, Stephen John
- Description:
- 37 p.
- ISBN:
- 0599873949
- Summary:
-
The braid groups Bn were introduced by Artin as a tool for studying knots. One of the many equivalent definitions of Bn is that it is the mapping class group of the disc with n puncture points. Using this definition, one can obtain a representation of Bn by letting it act on the homology of some space related to the n-times punctured disc. In this thesis we study two such representations, namely the Burau representation and the Lawrence-Krammer representation. We show that the Burau representation is not faithful for the braid group B 5, thus leaving B4 as the only remaining open case. We also show that the Lawrence-Krammer representation is faithful for all braid groups Bn, thus proving that the braid groups are linear and solving a long-standing open problem.
- Notes:
-
- (UnM)AAI9960470
- Source: Dissertation Abstracts International, Volume: 61-07, Section: B, page: 3620.
- Chair: Robion C. Kirby.
- Thesis (Ph.D.)--University of California, Berkeley, 2000.
- Reproduction:
- Microfiche. Ann Arbor, Mich.: University Microfilms International.
- Subject:
- Mathematics
- Other authors/contributors:
- University of California, Berkeley
- Copyright:
-
In Copyright
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Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 2000
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