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Zero Rotation Spectrum and Teichmüller Theory

  • Sang-hyun Kim
  • Thomas Koberda
  • Mahan Mj
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2231)

Abstract

In this chapter, we consider free group and surface group actions on the circle, and develop conditions under which the equivalence class of an action is determined by the rotation spectrum, and when the semi-conjugacy class of the action is determined by the marked rotation spectrum. In the case of indiscrete representations of groups into \( \operatorname {\mathrm {PSL}}_2(\mathbb {R})\), there is a lack of a geometric interpretation of such representations which is as well-developed as Teichmüller theory in the case of discrete representations. We will consider the degree to which marked rotation spectrum can supplant marked length spectrum as a (sometimes nearly complete) semi-conjugacy invariant.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sang-hyun Kim
    • 1
  • Thomas Koberda
    • 2
  • Mahan Mj
    • 3
  1. 1.School of MathematicsKorea Institute for Advanced StudySeoulRepublic of Korea
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  3. 3.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

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