Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16607 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914816317194240 |
|---|---|
| author | Lee, Donsung |
| author_facet | Lee, Donsung |
| contents | In 1974, Birman posed the question of under what conditions a matrix with Laurent polynomial entries is in the image of the Burau representation. In 1984, Squier observed that the matrices in the image are contained in a unitary group. In 2021, Salter formulated a specific question: whether the central quotient of the Burau image group is the central quotient of a certain subgroup of the unitary group. We solve this question negatively in the simplest nontrivial case, $n=3$, algorithmically constructing a counterexample. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Salter's question on the image of the Burau representation of $B_3$ Lee, Donsung Group Theory Geometric Topology 20F36, 20C99, 20E05 In 1974, Birman posed the question of under what conditions a matrix with Laurent polynomial entries is in the image of the Burau representation. In 1984, Squier observed that the matrices in the image are contained in a unitary group. In 2021, Salter formulated a specific question: whether the central quotient of the Burau image group is the central quotient of a certain subgroup of the unitary group. We solve this question negatively in the simplest nontrivial case, $n=3$, algorithmically constructing a counterexample. |
| title | Salter's question on the image of the Burau representation of $B_3$ |
| topic | Group Theory Geometric Topology 20F36, 20C99, 20E05 |
| url | https://arxiv.org/abs/2405.16607 |