On Translation Length of Anosov Maps on Curve Graph of Torus (joint with Hyungryul Baik, Changsub Kim, Hyunshik Shin) [arXiv:1908.00472] (submitted)

Abstract : We show that an Anosov map has a geodesic axis on the curve graph of a torus. The direct corollary of our result is the stable translation length of an Anosov map on the curve graph is always a positive integer. As the proof is constructive, we also provide an algorithm to calculate the exact translation length for any given Anosov map. The application of our result is threefold:

(a) to determine which word realizes the minimal translation length on the curve graph within a specific class of words,

(b) to establish the effective bound on the ratio of translation lengths of an Anosov map on the curve graph to that on Teichm├╝ller space, and

(c) to estimate the overall growth of the number of Anosov maps which have a sufficient number of Anosov maps with the same translation length.


*The QR code for the preprint is no longer available.

*Poster template courtesy of Mike Morrison #BetterPoster, and its LaTeX version is due to Rafael Balio.


Undergraduate Research Program Workshop(2019. 2. 22), KAIST

MAS491, Introduction to Contemporary Mathematics, KAIST