From the 1 of 6 linked papers with an AI index.
6 papers
The dark side of translation surfaces: It is not all about dynamics
Gianluca Faraco
The paper surveys translation surfaces from a geometric and topological perspective, covering definitions, moduli spaces, stratifications, period maps, and holonomy, and highlighti…
On the symplectic geometry of branched hyperbolic surfaces in genus two
Gianluca Faraco, Arnaud Maret
We construct analogues of Fenchel-Nielsen coordinates on an open and dense subset of the space of holonomies of branched hyperbolic structures on a closed genus-2 surface. We show…
Mapping class group orbit closures for Deroin-Tholozan representations
Yohann Bouilly, Gianluca Faraco, Arnaud Maret
We prove that infinite mapping class group orbits are dense in the character variety of Deroin-Tholozan representations. In other words, the action is minimal except for finite orb…
Isoperiodic foliation of the stratum
Gianluca Faraco, Guillaume Tahar, Yongquan Zhang
This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum . We prove that each leaf is a surface of infinite gen…
Simple loop conjecture for discrete representations in PSL
Gianluca Faraco, Subhojoy Gupta
We show that the Simple Loop Conjecture holds for any representation that is discrete but not faithful. That is, we show…
Relative period realization of holomorphic differentials with prescribed invariants
Dawei Chen, Gianluca Faraco
We provide a complete description of realizable relative period representations for holomorphic differentials on Riemann surfaces with prescribed orders of zeros and additional inv…