Geodesic
Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups
Joachim Schwermer1
1Universität Wien, Austria
Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 529-552

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DOI

We discuss the construction of totally geodesic cycles in locally symmetric spaces attached to arithmetic subgroups in algebraic groups G of type F4​ 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.
DOI : 10.4171/ggd/138
Classification : 11-XX, 22-XX, 57-XX, 00-XX
Mots-clés : Arithmetic groups, geometric cycles, cohomology, automorphic forms

Joachim Schwermer  1

1 Universität Wien, Austria 
Joachim Schwermer. Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups. Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 529-552. doi: 10.4171/ggd/138
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     author = {Joachim Schwermer},
     title = {Geometric cycles, {Albert} algebras and related cohomology classes for arithmetic groups},
     journal = {Groups, geometry, and dynamics},
     pages = {529--552},
     year = {2011},
     volume = {5},
     number = {2},
     doi = {10.4171/ggd/138},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/138/}
}
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