caa a22 4500 445884215 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9516-5 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9516-5 Waldner Christoph Department of Mathematics, University of Vienna, Nordbergstrae 15, 1090, Vienna, Austria aut Geometric cycles with local coefficients and the cohomology of arithmetic subgroups of the exceptional group G 2 [Elektronische Daten] [Christoph Waldner] We study the cohomology of a compact locally symmetric space attached to an arithmetic subgroup of a rational form of a group of type G 2 with values in a finite dimensional irreducible representation E of G 2. By constructing suitable geometric cycles and parallel sections of the bundle $${\tilde{E}}$$ we prove non-vanishing results for this cohomology. We prove all possible non-vanishing results compatible with the known vanishing theorems regarding unitary representations with non-zero cohomology in the case of the short fundamental weight of G 2. A decisive tool in our approach is a formula for the intersection numbers with local coefficients of two geometric cycles. Springer Science+Business Media B.V., 2010 Group cohomology nationallicence Arithmetic group nationallicence Intersection number nationallicence Exceptional group G 2 nationallicence Schur functor nationallicence Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 9-25 0046-5755 151:1<9 2011 151 10711 https://doi.org/10.1007/s10711-010-9516-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9516-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Waldner Christoph Department of Mathematics, University of Vienna, Nordbergstrae 15, 1090, Vienna, Austria aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 9-25 0046-5755 151:1<9 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer