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Tiling systems and homology of lattices in tree products

Lookup NU author(s): Professor Guyan Robertson

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Abstract

Let Γ be a torsion-free cocompact lattice in Aut(T1) × Aut(T2), where T1, T2 are trees whose vertices all have degree at least three. The group H2 (Γ, ℤ) is determined explicitly in terms of an associated 2-dimensional tiling system. It follows that under appropriate conditions the crossed product C* -algebra A associated with the action of Γ on the boundary of T1 × T2 satisfies rank Ko(A) = 2 · rank H2(Γ,ℤ).

Publication metadata

Author(s): Robertson G

Publication type: Article

Publication status: Published

Journal: New York Journal of Mathematics

Year: 2005

Volume: 11

Pages: 635-647

ISSN (print): 1076-9803

ISSN (electronic):

Publisher: Electronic Journals Project

URL: http://nyjm.albany.edu/j/2005/11-29.pdf

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