Groups, Geometry, and Dynamics


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Volume 5, Issue 2, 2011, pp. 529–552
DOI: 10.4171/GGD/138

Published online: 2011-03-06

Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups

Joachim Schwermer[1]

(1) Universit├Ąt Wien, Austria

We discuss the construction of totally geodesic cycles in locally symmetric spaces attached to arithmetic subgroups in algebraic groups $G$ of type $F_4$ which originate with reductive subgroups of the group $G$. In many cases, it can be shown that these cycles, to be called geometric cycles, yield non-vanishing (co)homology classes. Since the cohomology of an arithmetic group is related to the automorphic spectrum of the group, this geometric construction of non-vanishing classes leads to results concerning the existence of specific automorphic forms.

Keywords: Arithmetic groups, geometric cycles, cohomology, automorphic forms

Schwermer Joachim: Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups. Groups Geom. Dyn. 5 (2011), 529-552. doi: 10.4171/GGD/138