Dynnikov and train track transition matrices of pseudo-Anosov braids

S. Öykü Yurttaş

doi:10.3934/dcds.2016.36.541

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2016, Volume 36, Issue 1: 541-570. Doi: 10.3934/dcds.2016.36.541

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Dynnikov and train track transition matrices of pseudo-Anosov braids

S. Öykü Yurttaş^1,

1.
Dicle University, Mathematics Department, 21280, Diyarbakır

Received: April 30, 2014

Revised: April 30, 2015

Published: May 2017

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Abstract

We compare the spectra of Dynnikov matrices with the spectra of the train track transition matrices of a given pseudo-Anosov braid on the finitely punctured disk, and show that these matrices are isospectral up to roots of unity and zeros under some particular conditions. It is shown, via examples, that Dynnikov matrices are much easier to compute than transition matrices, and so yield data that was previously inaccessible.

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Mathematics Subject Classification: Primary: 37E30, 37B99; Secondary: 57M50.

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