Abstract

By "Hermitian locally symmetric space" we mean an arithmetic quotient of a bounded symmetric domain. Both the toroidal and the reductive Borel-Serre compactifications of such a space come equipped with canonical mappings to the Baily-Borel Satake compactification. In this article we show that there is a mapping from the toroidal compactification to the reductive Borel-Serre compactification, whose composition with the projection to the Baily-Borel compactification agrees with the canonical projection up to an arbitrarily small homotopy. We also consider arithmetic quotients of a self-adjoint homogeneous cone. There is a canonical mapping from the reductive Borel-Serre compactification to the standard compactification of such a locally symmetric cone. We show that this projection, when restricted to the closure of a polyhedral cone, has contractible fibers.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1095-1151
Launched on MUSE
1999-10-01
Open Access
No
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