Tits Geometry, Arithmetic Groups and the Proof of a Conjecture of Siegel

TL;DR

This paper demonstrates that certain locally symmetric spaces are quasi-isometric to Euclidean cones over finite simplicial complexes, providing a detailed metric analysis that proves a conjecture of Siegel.

Contribution

It establishes a quasi-isometric relationship for locally symmetric spaces and proves Siegel's conjecture through metric analysis.

Findings

Locally symmetric spaces are quasi-isometric to Euclidean cones over finite complexes.

The proof confirms Siegel's conjecture regarding these spaces.

Metric properties are key to understanding the geometric structure.

Abstract

We show that a locally symmetric space of noncompact type and with finite volume is quasi-isometric to the euclidean cone over a finite simplicial complex. A detailed analysis of metric properties yields a proof of a conjecture of Siegel.