# Nabil MehdiCadi Ayyad University | UCAM · Department of Mathematics

Nabil Mehdi

Doctor of Philosophy

## About

6

Publications

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Citations since 2017

## Publications

Publications (6)

Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on the manifold $M$ by diffeomorphisms one can define the $\Gamma$-co-invariant cohomology of $M$ to be the cohomology of the differential complex $\Omega_c(M)_\Gamma=\mathrm{span}\{\omega-\gamma^*\omega,\;\omega\in\Omega_c(M),\;\gamma\in\Gamma\}.$ For a Lie algebra $\mathcal{G}$ acting...

The first part of this thesis focuses on the theme of group actions on smooth manifolds and cohomology. Our contribution was to introduce a new differential subcomplex of the de Rham complex that can be attached to group actions on smooth manifolds, and which we call "The complex of co-invariant differential forms", we then study its cohomology as...

For an arbitrary real connected Lie group G we define \(\mathrm {p}(G)\) as the maximal integer p such that \(\mathbb {Z}^p\) is isomorphic to a discrete subgroup of G and \(\mathrm {q}(G)\) is the maximal integer q such that \(\mathbb {R}^q\) is isomorphic to a closed subgroup of G. The aim of this paper is to investigate properties of these two i...

Let $M$ be a smooth manifold and $\Gamma$ a group acting on $M$ by diffeomorphisms; which means that there is a group morphism $\rho:\Gamma\rightarrow \mathrm{Diff}(M)$ from $\Gamma$ to the group of diffeomorphisms of $M$. For any such action we associate a cohomology $\mathrm{H}(\Omega(M)_\Gamma)$ which we call the cohomology of $\Gamma$-coinvaria...