RESEARCH

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.

Slides

Lighting Talk @ 2019 Tech Topology Conference, Georgia Institute of Technology, USA

Lab/Research Seminar

  1. (03/22/2018)Curve complex of Torus
  2. (04/26/2018)Teichm├╝ller space of Torus
  3. (05/10/2018)Hyperbolicity of curve complex
  4. (05/31/2018)Translation length on curve graph
  5. (08/23/2018)Distances in curve graph
  6. (10/02/2018)[Masur-Minsky Series]I. Introduction and main results
  7. (10/31/2018)[Masur-Minsky Series]II. Outline of the proof of hyperbolicity

MAS532, Algebraic Topology II, KAIST

  1. (10/29/2018)Homotopy theory of fiber bundles

Posters

*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.

poster.pdf

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

MAS491, Introduction to Contemporary Mathematics, KAIST