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.


Additional Information

Print ISSN
pp. 1095-1151
Launched on MUSE
Open Access
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.