On type-preserving representations of the thrice punctured projective plane group
| Autor: | Sara Maloni, Tian Yang, Frederic Palesi |
|---|---|
| Přispěvatelé: | University of Virginia [Charlottesville], Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Department of Mathematics [Texas] (TAMU), Texas A&M University [College Station], University of Virginia, Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Fundamental group Algebra and Number Theory Group (mathematics) 010102 general mathematics Geometric Topology (math.GT) Dynamical Systems (math.DS) Type (model theory) 01 natural sciences Mapping class group Mathematics - Geometric Topology Character (mathematics) [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] FOS: Mathematics Geometry and Topology Projective plane Projective linear group Mathematics - Dynamical Systems 0101 mathematics Analysis Euler class Mathematics 57M05 57M50 30F60 20H10 |
| Zdroj: | Journal of Differential Geometry Journal of Differential Geometry, 2021, 119 (3), ⟨10.4310/jdg/1635368618⟩ |
| DOI: | 10.4310/jdg/1635368618⟩ |
| Popis: | In this paper we consider type-preserving representations of the fundamental group of the three--holed projective plane into $\mathrm{PGL}(2, \R) =\mathrm{Isom}(\HH^2)$ and study the connected components with non-maximal euler class. We show that in euler class zero for all such representations there is a one simple closed curve which is non-hyperbolic, while in euler class $\pm 1$ we show that there are $6$ components where all the simple closed curves are sent to hyperbolic elements and $2$ components where there are simple closed curves sent to non-hyperbolic elements. This answer a question asked by Brian Bowditch. In addition, we show also that in most of these components the action of the mapping class group on these non-maximal component is ergodic. In this work, we use an extension of Kashaev's theory of decorated character varieties to the context of non-orientable surfaces. Comment: 25 pages, 6 figures |
| Databáze: | OpenAIRE |
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