Journal article
The Kauffman bracket skein module at an irreducible representation
Quantum topology
06/28/2025
DOI: 10.4171/qt/241
Abstract
In this paper, we study the Kauffman bracket skein module of closed oriented three-manifolds at non-multiple-of-four roots of unity. Our main result establishes that the localization of these modules 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 to show that the dimension of the skein module of an oriented rational homology sphere with finite character variety and at most 2 -torsion in its first homology 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 such rational homology spheres with tame universal skein module.
Details
- Title: Subtitle
- The Kauffman bracket skein module at an irreducible representation
- Creators
- Mohammad Farajzadeh-TehraniCharles Frohman - University of IowaJoanna Kania-Bartoszynska - U.S. National Science Foundation
- Resource Type
- Journal article
- Publication Details
- Quantum topology
- DOI
- 10.4171/qt/241
- ISSN
- 1663-487X
- eISSN
- 1664-073X
- Publisher
- EUROPEAN MATHEMATICAL SOC-EMS; BERLIN
- Grant note
- NSF: DMS-2038103, DMS-2003340
This material is based upon work supported by NSF awards DMS-2038103 and DMS-2003340, and while serving at the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are thoseof the authors and do not necessarily reflect the views of the National Science Foundation.
- Language
- English
- Electronic publication date
- 06/28/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984843596202771
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