Explicit reduction theory for SU(2,1;Z[i])

2006/01/04 by Dan Yasaki, Yasaki, Dan
Mathematics · #11F57 (Primary) #53C35 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F57 #msc:53C35

paper · pdf · doi:10.48550/arxiv.math/0601071

26 pages, 5 figures

arxiv created 2006/01/04 · arxiv updated 2009/12/01

Abstract

Let Gamma\D be an arithmetic quotient of a symmetric space of non-compact type. A spine D₀ is a Gamma-equivariant deformation retraction of D with dimension equal to the virtual cohomological dimension of Gamma. We explicitly construct a spine for the case of Gamma=SU(2,1;Z[i]). The spine is then used to compute the cohomology of Gamma\D with various local coefficients.

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