Another point in homological algebra: Duality for discontinuous group actions

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dc.creatorGrunewald, F.
dc.creatorSinghof, W.
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:31:01Z
dc.date.available2026-07-07T12:31:01Z
dc.descriptionWe consider discontinuous operations of a group $G$ on a contractible $n$-dimensional manifold $X$. Let $E$ be a finite dimensional representation of $G$ over a field $k$ of characteristics 0. Let $\mathcal{E}$ be the sheaf on the quotient space $Y=G \setminus X$ associated to $E$. Let $H^{\bullet}_{\textbf{!}}(Y;\mathcal{E})$ be the image in $H^{\bullet}(Y;\mathcal{E})$ of the cohomology with compact support. In the cases where both $H^{\bullet}_{\textbf{!}}(Y;\mathcal{E})$ and $H^{\bullet}_{\textbf{!}}(Y;\mathcal{E}^*)$ ($\mathcal{E}^*$ being the the sheaf associated to the representation dual to $E$) are finite dimensional, we establish a non-degenerate duality between $H^{m}_{\textbf{!}}(Y;\mathcal{E})$ and $H^{n-m}_{\textbf{!}}(Y;\mathcal{E}^{\ast})$. We also show that this duality is compatible with Hecke operators.
dc.identifierhttps://arxiv.org/abs/0901.2417
dc.identifierhttp://arxiv.org/abs/0901.2417
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216314
dc.subjectAlgebraic Topology
dc.subject20J05, 11F06
dc.titleAnother point in homological algebra: Duality for discontinuous group actions
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