@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ In this thesis, we are interested in computing the foliated Dolbeault cohomology groups H0∗L (M) for some complex laminations. This amounts to solving the problem of the ∂ along the leaves ∂Lα = ω. (Here M is a metric space or a differentiable manifold if L is a foliation F.) Three situations were considered explicitly.1. Let M = Ω be an open set of C×R equipped with the foliation F whose leaves are the sections Ωt = {z ∈ C(z, t) ∈ Ω}; we say that F is the canonical foliation of Ω. Under certain conditions on Ω and growth conditions on the foliated form ω, we show that the equation ∂Fα = ω has a solution.2. Let (αn)n≥1 be a sequence of real numbers, strictly increasing with α1 = −1 and converging to 1. In C × R we consider the points A = (0, 1) and An = (0, αn) for n ≥ 1. For all n ≥ 1, let Sn be the sphere of C × R with a diameter segment [AnA] and E the union of all these spheres. Then E is a compact and connected subset of C × R. Let γ : E −→ E the homeomorphism defined by γ(w,u) = (ρn(w),u), where (w,u) ∈ Sn and ρn is the rotation in C with angle 2πn. The suspension of γ gives rise to a complex lamination L whose leaves are all equivalent Riemann surfaces isomorphic to C∗. For This example we show that the vector space H01 (L) is zero.3. Consider the manifold M = C × Rn \\ {(0, 0)} (the coordinates of a point are denoted (z,t)) endowed with the complex foliation F defined by the differential system dt1 = • • • = dn = 0. The diffeomorphism γ : (z, t) ∈ M −→ (λz, λt) ∈ M (where 0 < λ < 1) acts on M freely and properly ; moreover it is an automorphism of the complex foliation F ; then F induces on the quotient M = M/γ (which is diffeomorphic to S n+1 × S1) a complex foliation F by Riemann surfaces. All leaves are isomorphic to C except one of them which is an elliptic curve. We show that the vector spaces H00 F (M) and H01F (M) of foliated Dolbeault cohomology are isomorphic to C. """ ; dct:identifier "NNT: 2013VALE0010" ; dct:issued "2026-05-09T10:15:50.444283"^^xsd:dateTime ; dct:language "fr" ; dct:modified "2026-05-09T10:15:50.444287"^^xsd:dateTime ; dct:publisher ; dct:title "Cohomology of some complex laminations" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "cohomologie-des-groupes", "cohomologie-feuilletee", "cohomology-groups", "feuilletage", "foliated-cohomology", "foliation", "infoeu-reposemanticsdoctoralthesis", "lamination", "le--le-long-des-feuilles", "mathmath-gmmathematics-mathgeneral-mathematics-mathgm", "spiotherengineering-sciences-physicsother", "the--along-the-leaves", "theses" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-05-09T10:15:50.474186"^^xsd:dateTime ; dct:modified "2026-05-09T10:15:50.427210"^^xsd:dateTime ; dct:title "Cohomology of some complex laminations" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .