The moduli space of marked generalized cusps in real projective manifolds

Ballas, Samuel; Cooper, Daryl; Leitner, Arielle

doi:10.1090/ecgd/367

The moduli space of marked generalized cusps in real projective manifolds
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by Samuel A. Ballas, Daryl Cooper and Arielle Leitner

Conform. Geom. Dyn. 26 (2022), 111-164

DOI: https://doi.org/10.1090/ecgd/367

Published electronically: August 17, 2022

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Abstract:

ln this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to $M\times [0,\infty )$ where $M$ is a closed Euclidean manifold. These are classified by Ballas, Cooper, and Leitner [J. Topol. 13 (2020), pp. 1455-1496]. The marked moduli space is homeomorphic to a subspace of the space of conjugacy classes of representations of $\pi _1M$. It has one description as a generalization of a trace-variety, and another description involving weight data that is similar to that used to describe semi-simple Lie groups. It is also a bundle over the space of Euclidean similarity (conformally flat) structures on $M$, and the fiber is a closed cone in the space of cubic differentials. For $3$-dimensional orientable generalized cusps, the fiber is homeomorphic to a cone on a solid torus.

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