Geometry & Topology Volume 12, issue 3 (2008)

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ISSN 1364-0380 (online)

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Minimality of the well-rounded retract

Alexandra Pettet and Juan Souto

Geometry & Topology 12 (2008) 1543–1556

DOI: 10.2140/gt.2008.12.1543

Abstract

We prove that the well-rounded retract of ${SO}_{n} ∖ {SL}_{n} ℝ$ is a minimal ${SL}_{n} ℤ$ –invariant spine.

Keywords

well-rounded retract, symmetric space, systole, deformation retract, lattice

Mathematical Subject Classification 2000

Primary: 20F65

Secondary: 12G10, 53C35, 11F75

References

Publication

Received: 1 December 2007

Revised: 18 April 2008

Accepted: 27 April 2008

Published: 10 June 2008

Proposed: Benson Farb

Seconded: Walter Neumann, Martin Bridson

Authors

Alexandra Pettet
Department of Mathematics Stanford University Stanford California 94305 USA

Juan Souto
Department of Mathematics University of Michigan Ann Arbor Michigan 48109 USA