Leslie Saper

Tilings and finite energy retractions of locally symmetric spaces

Abstract. Let

The fundamental group of reductive Borel–Serre and Satake compactifications

\Gamma \backslash \overline{X}

L 2 -Cohomology of Arithmetic Varieties

be the Borel-Serre compactifiction of an arithmetic quotient

L2-cohomology of arithmetic varieties

\Gamma \backslash X

Intersection cohomology of cs-spaces and Zeeman's filtration

of a symmetric space of noncompact type. We construct natural tilings

L-modules and the Conjecture of Rapoport and Goresky-MacPherson

\Gamma \backslash \overline{X} = \coprod _P \Gamma \backslash \overline{X}_P

L-modules and micro-support

(depending on a parameter b) which generalize the Arthur-Langlands partition of

On the Cohomology of Locally Symmetric Spaces and of their Compactifications

\Gamma \backslash X

Geometric rationality of equal-rank Satake compactifications

. This is applied to yield a natural piecewise analytic deformation retraction of

Perverse sheaves and the reductive Borel-Serre compactification

\Gamma \backslash \overline{X}