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Homological representations of braid groups [microform]
Bib ID 3284042
Format MicroformMicroform, BookBook
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. 
Subjects Mathematics.
Other authors/contributors University of California, Berkeley

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