A closed ball compactification of a maximal component via cores of trees

Giuseppe Martone; Charles Ouyang; Andrea Tamburelli

doi:10.2140/agt.2024.24.3693

A closed ball compactification of a maximal component via cores of trees

Giuseppe Martone
, Charles Ouyang
, Andrea Tamburelli

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that, in the character variety of surface group representations into the Lie group PSL(2,ℝ) × PSL(2,ℝ), the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as (Formula presented)–valued mixed structures.

Original language	English
Pages (from-to)	3693-3717
Number of pages	25
Journal	Algebraic and Geometric Topology
Volume	24
Issue number	7
DOIs	https://doi.org/10.2140/agt.2024.24.3693
State	Published - 2024

Keywords

Harmonic maps
Hyperbolic surfaces
Quadratic differentials
Teichmüller theory
ℝ–trees

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10.2140/agt.2024.24.3693

Cite this

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title = "A closed ball compactification of a maximal component via cores of trees",

abstract = "We show that, in the character variety of surface group representations into the Lie group PSL(2,ℝ) × PSL(2,ℝ), the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as (Formula presented)–valued mixed structures.",

keywords = "Harmonic maps, Hyperbolic surfaces, Quadratic differentials, Teichm{\"u}ller theory, ℝ–trees",

author = "Giuseppe Martone and Charles Ouyang and Andrea Tamburelli",

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AU - Ouyang, Charles

AU - Tamburelli, Andrea

PY - 2024

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N2 - We show that, in the character variety of surface group representations into the Lie group PSL(2,ℝ) × PSL(2,ℝ), the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as (Formula presented)–valued mixed structures.

AB - We show that, in the character variety of surface group representations into the Lie group PSL(2,ℝ) × PSL(2,ℝ), the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as (Formula presented)–valued mixed structures.

KW - Harmonic maps

KW - Hyperbolic surfaces

KW - Quadratic differentials

KW - Teichmüller theory

KW - ℝ–trees

UR - https://www.scopus.com/pages/publications/85213726717

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M3 - Article

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JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 7

ER -

A closed ball compactification of a maximal component via cores of trees

Abstract

Keywords

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