Dr. Daniele Alessandrini
Project leader
Stevens Institute of Technology
E-mail: daniele.alessandrini(at)gmail.com
Homepage: https://daniele-math.github.io/
Project
1Hitchin components for orbifolds
Publications within SPP2026
We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichmüller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball and we compute its dimension explicitly. We then give applications to the study of the pressure metric, cyclic Higgs bundles, and the deformation theory of real projective structures on 3-manifolds.
| Journal | Journal of the European Mathematical Society |
| Link to preprint version | |
| Link to published version |
Related project(s):
1Hitchin components for orbifolds
Geometric structures on manifolds became popular when Thurston used them in his work on the Geometrization Conjecture. They were studied by many people and they play an important role in Higher Teichmüller Theory. Geometric structures on a manifold are closely related with representations of the fundamental group and with flat bundles. Higgs bundles can be very useful in describing flat bundles explicitly, via solutions of Hitchin's equations. Baraglia has shown in his Thesis that this technique can be used to construct geometric structures in interesting cases. Here we will survey some recent results in this direction, which are joint work with Qiongling Li.
Related project(s):
1Hitchin components for orbifolds