JournalsggdVol. 5, No. 2pp. 529–552

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

  • Joachim Schwermer

    Universität Wien, Austria
Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups cover
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Abstract

We discuss the construction of totally geodesic cycles in locally symmetric spaces attached to arithmetic subgroups in algebraic groups GG of type F4F_4 which originate with reductive subgroups of the group GG. 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.

Cite this article

Joachim Schwermer, Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 529–552

DOI 10.4171/GGD/138