The Moduli Space of Generalized Cusps in Real Projective Manifolds.

Geometry & Topology
Event time: 
Tuesday, April 23, 2019 - 4:15pm
DL 431
Daryl Cooper
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Event description: 

 In the study of hyperbolic 3-manifolds cusps play an important role. The geometry of  a cusp is determined by a similarity structure on the boundary of the cusp. In the finite volume  case, the boundary is a torus and the similarity structure is determined by a complex number with  positive imaginary part. Properly-convex real-projective manifolds are a generalization of hyperbolic manifolds. In dimension 3 the moduli space of generalized cusps is a bundle over the space of similarity structures on the torus, with fiber a subspace of the space of (real) cubic differentials. Conjecturally a similar statement is true in all dimensions for cusps with compact boundary. There is a 9-dimensional cusp with fundamental group the integer Heisenberg group,  and the classification of cusps with non-compact boundary is unknown.  Joint: Sam Ballas, Arielle Leitner.

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