An algorithm to compute the Teichmueller polynomial from matrices

Abstract

In their precedent work, the authors constructed closed oriented hyperbolic surfaces with pseudo-Anosov homeomorphisms from certain class of integral matrices. In this paper, we present a very simple algorithm to compute the Teichmueller polynomial corresponding to those surface homeomorphisms by first constructing an invariant track whose first homology group can be naturally identified with the first homology group of the surface, and computing its Alexander polynomial.

The exposition has been improved: the second half of the introduction and the proof of the key proposition (Proposition 2) were rewritten with greater details. Section 2 and an appendix by KyeongRo Kim and TaeHyouk Jo were added to give a better explanation of the set up. 17 pages, 6 figures

References in corpus (3)

• Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior
• Constructing pseudo-Anosov maps with given dilatations
• Computing the Teichmueller polynomial