Preprint
The Kauffman Bracket Skein Module at an irreducible representation
arXiv.org
Cornell University
02/26/2024
DOI: 10.48550/arxiv.2402.17037
Abstract
in this paper, we study the Kauffman bracket skein module of closed oriented three-manifolds at a non-multiple-of-four roots of unity. Our main result establishes that the localization of this module at a maximal ideal, which corresponds to an irreducible representation of the fundamental group of the manifold, forms a one-dimensional free module over the localized unreduced coordinate ring of the character variety. We apply this by proving that the dimension of the skein module of a homology sphere with finite character variety, when the order of the root of unity is not divisible by 4, is greater than or equal to the dimension of the unreduced coordinate ring of the character variety. This leads to a computation of the dimension of the skein module with coefficients in rational functions for homology spheres with tame universal skein module.
Details
- Title: Subtitle
- The Kauffman Bracket Skein Module at an irreducible representation
- Creators
- Mohammad Farajzadeh-TehraniCharles FrohmanJoanna Kania-Bartoszynska
- Resource Type
- Preprint
- Publication Details
- arXiv.org
- DOI
- 10.48550/arxiv.2402.17037
- eISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 02/26/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984563558502771
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