Geodesic
A closed ball compactification of a maximal component via cores of trees
Martone, Giuseppe1 ; Ouyang, Charles2 ; Tamburelli, Andrea3
1 Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX, United States
2 Department of Mathematics, Washington University, St Louis, MO, United States
3 Department of Mathematics, University of Pisa, Pisa, Italy
Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3693-3717

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 ( A1×A1 ¯,2)–valued mixed structures.

DOI : 10.2140/agt.2024.24.3693
Keywords: harmonic maps, hyperbolic surfaces, Teichmüller theory, $\mathbb{R}$–trees, quadratic differentials

Martone, Giuseppe 1 ; Ouyang, Charles 2 ; Tamburelli, Andrea 3

1 Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX, United States
2 Department of Mathematics, Washington University, St Louis, MO, United States
3 Department of Mathematics, University of Pisa, Pisa, Italy 
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Martone, Giuseppe; Ouyang, Charles; Tamburelli, Andrea. A closed ball compactification of a maximal component via cores of trees. Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3693-3717. doi: 10.2140/agt.2024.24.3693

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