Journal of the Mathematical Society of Japan

Geometry of the Gromov product: Geometry at infinity of Teichmüller space

Hideki MIYACHI

Abstract

This paper is devoted to studying transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptotic behavior of the Gromov product in hyperbolic spaces. We characterize a quotient semigroup of such transformations on Teichmüller space by use of simplicial automorphisms of the complex of curves, and we will see that such transformation is recognized as a “coarsification” of isometries on Teichmüller space which is rigid at infinity. We also show a hyperbolic characteristic that any finite dimensional Teichmüller space does not admit (quasi)-invertible rough-homothety.

Article information

Source
J. Math. Soc. Japan, Volume 69, Number 3 (2017), 995-1049.

Dates
First available in Project Euclid: 12 July 2017

https://projecteuclid.org/euclid.jmsj/1499846515

Digital Object Identifier
doi:10.2969/jmsj/06930995

Mathematical Reviews number (MathSciNet)
MR3685033

Zentralblatt MATH identifier
1378.30018

Citation

MIYACHI, Hideki. Geometry of the Gromov product: Geometry at infinity of Teichmüller space. J. Math. Soc. Japan 69 (2017), no. 3, 995--1049. doi:10.2969/jmsj/06930995. https://projecteuclid.org/euclid.jmsj/1499846515

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