| | |
| | |
Stat |
Members: 3645 Articles: 2'504'928 Articles rated: 2609
25 April 2024 |
|
| | | |
|
Article overview
| |
|
On the image of the Lawrence-Krammer representation | Ryan Budney
; | Date: |
23 Feb 2002 | Subject: | Geometric Topology MSC-class: 20F36;57M60;20C99 | math.GT | Abstract: | A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant unit complex numbers, then the form is negative-definite Hermitian. Since unitary matrices diagonalize, the conjugacy class of a matrix in the unitary group is determined by its eigenvalues. It is shown that the eigenvalues of a Lawrence-Krammer matrix satisfy some symmetry relations. Using the fact that non-invertible knots exist, the symmetry relations imply that there are matrices in the image of the Lawrence-Krammer representation that are conjugate in the unitary group, yet the braids that they correspond to are not conjugate. The two primary tools involved in constructing the form are Bigelow’s interpretation of the Lawrence-Krammer representation, together with Morse theory on manifolds with corners. | Source: | arXiv, math.GT/0202246 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |