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Computation of the taut, the veering and the Teichmüller polynomials

2020/09/28 by Anna Parlak, Parlak, Anna
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.2009.13558

32 pages, 15 figures, 5 algorithms. In version 2 we no longer consider modules obtained by the extension of scalars. The algorithm for the computation of the Teichmuller polynomial is corrected. In the previous version in some cases the output had a redundant linear factor

arxiv created 2021/01/20 · arxiv updated 2021/01/22

Abstract

Landry, Minsky and Taylor [LMT] introduced two polynomial invariants of veering triangulations -- the taut polynomial and the veering polynomial. We give algorithms to compute these invariants. In their definition [LMT] use only the upper track of the veering triangulation, while we consider both the upper and the lower track. We prove that the lower and the upper taut polynomials are equal. However, we show that there are veering triangulations whose lower and upper veering polynomials are different. [LMT] related the Teichmüller polynomial of a fibred 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 fibred face of the Thurston norm ball.

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