The Gilmer-Masbaum map is not injective on the Kauffman bracket skein module
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912590864580608 |
|---|---|
| author | Kitaeff, Edwin |
| author_facet | Kitaeff, Edwin |
| contents | Gilmer and Masbaum use Witten-Reshetikhin-Turaev (WRT) invariants to define a map from the Kauffman bracket skein module to a set of complex-valued functions defined on roots of unity in order to provide a lower bound for its dimension. We compute the image of the evaluation map for a family of mapping tori of the 2-torus and find that the restriction of the map to certain homology classes is not injective. This provides an answer to a question posed by Gilmer and Masbaum in the latter paper. Moreover, we give a basis for the Kauffman bracket skein module in the case of the mapping torus of a power of the Dehn twist along the meridian of the 2-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gilmer-Masbaum map is not injective on the Kauffman bracket skein module Kitaeff, Edwin Geometric Topology 57K31 Gilmer and Masbaum use Witten-Reshetikhin-Turaev (WRT) invariants to define a map from the Kauffman bracket skein module to a set of complex-valued functions defined on roots of unity in order to provide a lower bound for its dimension. We compute the image of the evaluation map for a family of mapping tori of the 2-torus and find that the restriction of the map to certain homology classes is not injective. This provides an answer to a question posed by Gilmer and Masbaum in the latter paper. Moreover, we give a basis for the Kauffman bracket skein module in the case of the mapping torus of a power of the Dehn twist along the meridian of the 2-torus. |
| title | The Gilmer-Masbaum map is not injective on the Kauffman bracket skein module |
| topic | Geometric Topology 57K31 |
| url | https://arxiv.org/abs/2410.23153 |