In this article, we propose an Outer space analog for the principal stratum of the unit tangent bundle to the Teichmüller space T(S) of a closed hyperbolic surface S. More specifically, we focus on properties of the geodesics in Teichmüller space determined by the principal stratum. We show that the analogous Outer space "principal" periodic geodesics share certain stability properties with the principal stratum geodesics of Teichmüller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichmüller space context.
|Number of pages||30|
|Journal||International Mathematics Research Notices|
|State||Published - 1 Jul 2019|
Bibliographical noteFunding Information:
This work was supported by U.S. National Science Foundation grants [DMS 1107452, 1107263, 1107367] “RNMS: Geometric structures And Representation varieties” (the GEAR Network); ISF grant [1941/14 to Y.A.-K.]; NSF grants [DMS-1405146 and DMS-1710868 to I.K.].
This article arose in response to a question of Lee Mosher. The authors would like to thank Mladen Bestvina, Chris Leininger, Joseph Maher, Lee Mosher, and Kasra Rafi for helpful and interesting conversations, as well as the MSRI for its hospitality. The authors acknowledge support from U.S. National Science Foundation. All three authors acknowledge the support of the Mathematical Sciences Research Institute during the Fall 2017 semester.
© 2018 The Author(s). Published by Oxford University Press. All rights reserved.
ASJC Scopus subject areas
- Mathematics (all)