Cohomologie feuillet\'ee du flot affine de Reeb sur la vari\'et\'e de Hopf
AEK Alaoui - arXiv preprint arXiv:1909.11963, 2019 - arxiv.org
AEK Alaoui
arXiv preprint arXiv:1909.11963, 2019•arxiv.orgWe determine explicitly the foliated cohomology $ H_ {\cal F}^\ast (M) $ of the affine Reeb
flow ${\cal F} $ on the Hopf manifold ${\Bbb S}^ n\times {\Bbb S}^ 1$. The vector space $ H_
{\cal F}^ 1 (M) $ contains exactly the obstructions to solve the cohomological equation $
X\cdot f= g $ where $ f $ and $ g $ are $ C^\infty $-functions and $ X $ is any non singular
vector field defining the foliation ${\cal F} $. The topological dual of $ H_ {\cal F}^ 1 (M) $ is
the space of distributions invariant by $ X $.
flow ${\cal F} $ on the Hopf manifold ${\Bbb S}^ n\times {\Bbb S}^ 1$. The vector space $ H_
{\cal F}^ 1 (M) $ contains exactly the obstructions to solve the cohomological equation $
X\cdot f= g $ where $ f $ and $ g $ are $ C^\infty $-functions and $ X $ is any non singular
vector field defining the foliation ${\cal F} $. The topological dual of $ H_ {\cal F}^ 1 (M) $ is
the space of distributions invariant by $ X $.
We determine explicitly the foliated cohomology of the affine Reeb flow on the Hopf manifold . The vector space contains exactly the obstructions to solve the cohomological equation where and are -functions and is any non singular vector field defining the foliation . The topological dual of is the space of distributions invariant by .
arxiv.org