Complex hyperbolic reflection groups and lattices

Project: Research project

Description

Scope of work Julien Paupert The PI proposes to continue at Arizona State University the research projects detailed in the proposal. Namely, the proposed research is a systematic investigation of (real and complex) reflection groups in PU(n, 1), particularly discrete subgroups and lattices.The main goal is to obtain new discrete subgroups and lattices in PU(2, 1), more specifically many new non-arithmetic lattices. The PI will continue working on all of the aspects described in the proposal, namely: Non-arithmetic lattices in generated by higher-order complex reflections (main project, joint with M. Deraux, University of Grenoble, France, and J. Parker, Durham University, UK). Discrete groups and lattices generated by 2 regular elliptic isometries; decomposable pairs (joint with P. Will, University of Grenoble, France). Finite real reflection groups (joint with E. Falbel, University of Paris 6, France). Elementary complex hyperbolic geometry: invariants of complex hyperbolic triangles and convex hulls of finitely many points in complex hyperbolic space (joint with D. Toledo, University of Utah). 1
StatusFinished
Effective start/end date5/7/126/30/14

Funding

  • National Science Foundation (NSF): $65,819.00

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Hyperbolic Groups
Reflection Group
Discrete Subgroup
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Complex Reflection Groups
Complex Hyperbolic Space
Lobachevskian geometry
Discrete Group
Decomposable
Isometry
Convex Hull
Triangle
Higher Order
Invariant