Groups, Geometry, and Dynamics


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Volume 10, Issue 4, 2016, pp. 1211–1225
DOI: 10.4171/GGD/380

Published online: 2017-01-26

Closed orbits for the diagonal group and well-rounded lattices

Michael Levin[1], Uri Shapira[2] and Barak Weiss[3]

(1) Ben Gurion University, Be-er Sheva, Israel
(2) Technion, Haifa, Israel
(3) Tel Aviv University, Israel

Curt McMullen showed that every compact orbit for the action of the diagonal group on the space of lattices contains a well-rounded lattice. We extend this to all closed orbits.

Keywords: Closed orbits, diagonal group, well-rounded lattices

Levin Michael, Shapira Uri, Weiss Barak: Closed orbits for the diagonal group and well-rounded lattices. Groups Geom. Dyn. 10 (2016), 1211-1225. doi: 10.4171/GGD/380