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On the existence of spines for Q-rank 1 groups

Dan Yasaki
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Abstract

Let X=Gamma\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Gamma-equivariant deformation retractions of D=G/K onto a set D_0. We prove that D_0 is a spine, having dimension equal to the virtual cohomological dimension of Gamma. In fact, there is a (k-1)-parameter family of such deformations retractions, where k is the number of Gamma-conjugacy classes of rational parabolic subgroups of G. The construction of the spine also gives a way to construct an exact fundamental domain for Gamma.

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Dan Yasaki. 2006-01-04. On the existence of spines for Q-rank 1 groups. https://arxiv.org/abs/math/0601073

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