The Real Spectrum Compactification of Character Varieties and its Relationship with Other Compactifications (Victor Jaeck, ETHZ)

14.10.2025 10:30

We study the moduli space of marked hyperbolic surfaces and related objects. Thurston shows that this space can be identified with the space of faithful and discrete representations of a finitely generated group in PSL(2,R), up to post-conjugation by PSL(2,R). This space is a key connected component of the character variety.
In this seminar, we examine degenerations of these representations by studying compactifications of the character variety. In particular, we present the real spectrum compactification, its topological properties, and show that it projects continuously onto the oriented Gromov equivariant compactification of the character variety, defined by Maxime Wolff. To this end, we interpret its boundary points geometrically and associate group actions on oriented real trees with them.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 14.10.2025, Séminaire "Groupes et géométrie"

entrée libre