[Sur les groupes de cohomologie de certains quotients de produits de demi-plans et demi-espaces supérieurs]
Un théorème de Matsushima et Shimura montre que l'espace des formes différentielles harmoniques sur un quotient compact d'un produit de demi-plans supérieurs sous l'action de certains groupes est la somme directe de deux sous-espaces appelés sous-espaces universel et cuspidal. Nous généralisons ce résultat aux quotients compacts d'un produit de demi-plans supérieurs et demi-espaces supérieurs (hyperboliques de dimension 3) sous l'action de certains groupes, obtenant une décomposition similaire.
A theorem of Matsushima–Shimura shows that the space of harmonic differential forms on the quotient of products of upper half planes under the action of certain groups, when the quotient is compact, is the direct sum of two subspaces called the universal and cuspidal subspaces. We generalize this result to compact quotients of products of upper half planes and upper half spaces (hyperbolic three spaces) under the action of certain groups to obtain a similar decomposition.
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@article{CRMATH_2017__355_9_937_0, author = {Agashe, Amod and Eldredge, Lydia}, title = {On the cohomology groups of certain quotients of products of upper half planes and upper half spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {937--941}, publisher = {Elsevier}, volume = {355}, number = {9}, year = {2017}, doi = {10.1016/j.crma.2017.04.016}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2017.04.016/} }
TY - JOUR AU - Agashe, Amod AU - Eldredge, Lydia TI - On the cohomology groups of certain quotients of products of upper half planes and upper half spaces JO - Comptes Rendus. Mathématique PY - 2017 SP - 937 EP - 941 VL - 355 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.04.016/ DO - 10.1016/j.crma.2017.04.016 LA - en ID - CRMATH_2017__355_9_937_0 ER -
%0 Journal Article %A Agashe, Amod %A Eldredge, Lydia %T On the cohomology groups of certain quotients of products of upper half planes and upper half spaces %J Comptes Rendus. Mathématique %D 2017 %P 937-941 %V 355 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.04.016/ %R 10.1016/j.crma.2017.04.016 %G en %F CRMATH_2017__355_9_937_0
Agashe, Amod; Eldredge, Lydia. On the cohomology groups of certain quotients of products of upper half planes and upper half spaces. Comptes Rendus. Mathématique, Tome 355 (2017) no. 9, pp. 937-941. doi : 10.1016/j.crma.2017.04.016. http://www.numdam.org/articles/10.1016/j.crma.2017.04.016/
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