## 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.## References

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## Bibliographic Information

**Samuel A. Ballas**- Affiliation: Florida State University
- MR Author ID: 1084949
- ORCID: 0000-0003-3340-3853
- Email: ballas@math.fsu.edu
**Daryl Cooper**- Affiliation: University of California, Santa Barbara
- MR Author ID: 239760
- Email: cooper@math.ucsb.edu
**Arielle Leitner**- Affiliation: Afeka College of Engineering
- MR Author ID: 907776
- Email: ariellel@afeka.ac.il
- Received by editor(s): March 6, 2021
- Published electronically: August 17, 2022
- Additional Notes: The first author was partially supported by the NSF grant DMS-1709097. The second author was partially supported by the University of Sydney Mathematics Research Institute (SMRI). The third author was partially supported by ISF grant 704/08.
- © Copyright 2022 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**26**(2022), 111-164 - MSC (2020): Primary 22-02, 51-02, 57-02
- DOI: https://doi.org/10.1090/ecgd/367
- MathSciNet review: 4470161