Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
3-pleated surfaces
In joint work with Maloni, Mazzoli, and Zhang, we introduced a notion of pleated surfaces for the higher rank Lie group PGL(d,C). These are homomorphisms from a surface group into PGL(d,C) which, in particular, are Anosov along the leaves of a maximal geodesic lamination. We parametrized the space of such d-pleated surfaces using generalized shear-bend cocycles. Moreover, we showed that for each maximal geodesic lamination L, each connected component of the PGL(d,C)-representation variety contains exactly one connected component of the space of PGL(d,C)-conjugacy classes of d-pleated surfaces with pleating locus L. In this talk, I will focus on the case d=3, to highlight some of the key challenges and ideas in our work.
No Notes/Supplements Uploaded