Minimality of the well-rounded retract

TL;DR

This paper proves that the well-rounded retract of the symmetric space associated with SO_n and SL_n(R) is a minimal invariant spine under the action of SL_n(Z), contributing to the understanding of geometric structures in number theory.

Contribution

It establishes the minimality of the well-rounded retract as an SL_n(Z)-invariant spine, a new result in the geometric analysis of symmetric spaces.

Findings

The well-rounded retract is a minimal SL_n(Z)-invariant spine.

The proof advances the understanding of geometric structures in number theory.

The result has implications for the topology of arithmetic groups.

Abstract

We prove that the well-rounded retract of SO_n\SL_n(R) is a minimal SL_n(Z)-invariant spine.