@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ The framework of this study is a closed manifold of dimension at least six that is provided with a nonzero De Rham cohomology class. The aim is to create tools to address the next problem: two closed non-singular (without zeroes) 1-forms in the fixed class are always isotopic? The general answer to the question is no, and a K-theoretical obstruction is expected. It is always possible to connect two non-singular closed 1-forms by a path that remains in the cohomology class; the isotopy of the two ends of the path is equivalent to find a relative homotopy of the path to another one made of non-singular 1-forms only. We introduce two kinds of pseudo-gradients for each positive number L: those with an L-elementary link and those that we call L-transverse. They form a class of vector fields adapted to the 1-forms that allows to do an algebraic reading associated with the path. This reading is similar to that made in the theory of Hatcher-Wagoner who treated the isotopy problem of real-valued functions without critical points. We manage to find L, a number large enough to deform a path of 1-forms with only two critical indices into another one with an L-transverse equipment in normal form. The zeroes of such a path that are born together, die together and moreover, the associated Cerf-Novikov graphic is closed : the cited algebraic reading belongs to some K_2, which is the starting point for the definition of an obstruction for two non-singular closed 1-forms to be isotopic. """ ; dct:identifier "tel-00768575" ; dct:issued "2026-05-29T12:47:23.118748"^^xsd:dateTime ; dct:language "fr" ; dct:modified "2026-05-29T12:47:23.118758"^^xsd:dateTime ; dct:publisher ; dct:title "Contribution to a parametrised Morse-Novikov theory" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "1-forme-fermee", "adapted-pseudo-gradient", "algebraic-k-theory", "cerfs-graphic", "closed-1-form", "complexe-de-morse-novikov", "glissement-danse", "graphique-de-cerf", "handle-slide", "infoeu-reposemanticsdoctoralthesis", "k-theorie-algebrique", "mathmath-gtmathematics-mathgeometric-topology-mathgt", "morse-novikov-complex", "pseudo-gradient-adapte", "pseudo-isotopie", "pseudo-isotopy", "theses", "transversalite", "transversality" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-05-29T12:47:23.145360"^^xsd:dateTime ; dct:modified "2026-05-29T12:47:23.029015"^^xsd:dateTime ; dct:title "Contribution to a parametrised Morse-Novikov theory" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .