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Computation of the Taut, the Veering and the Teichmüller polynomials
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Parlak, Anna (2021) Computation of the Taut, the Veering and the Teichmüller polynomials. Experimental Mathematics . doi:10.1080/10586458.2021.1985656 ISSN 1944-950X. (In Press)
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Official URL: https://doi.org/10.1080/10586458.2021.1985656
Abstract
Landry, Minsky and Taylor (LMT) introduced two polynomial invariants of veering triangulations—the taut polynomial and the veering polynomial. Here, we consider a pair of taut polynomials associated to one veering triangulation, the upper and the lower one, and analogously the upper and lower veering polynomials. We prove that the upper and lower taut polynomials are equal. In contrast, the upper and lower veering polynomials of the same veering triangulation may differ by more than a unit. We give algorithms to compute all these invariants. LMT related the Teichmüller polynomial of a fibered face of the Thurston norm ball with the taut polynomial of the associated layered veering triangulation. We use this result to give an algorithm to compute the Teichmüller polynomial of any fibered face of the Thurston norm ball.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| SWORD Depositor: | Library Publications Router | ||||||
| Library of Congress Subject Headings (LCSH): | Three-manifolds (Topology), Triangulation , Polynomials | ||||||
| Journal or Publication Title: | Experimental Mathematics | ||||||
| Publisher: | Taylor & Francis | ||||||
| ISSN: | 1944-950X | ||||||
| Official Date: | 21 October 2021 | ||||||
| Dates: |
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| DOI: | 10.1080/10586458.2021.1985656 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 3 November 2021 | ||||||
| Date of first compliant Open Access: | 3 November 2021 | ||||||
| RIOXX Funder/Project Grant: |
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