Multivalued functionals, one-forms and deformed de Rham complex

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dc.creatorMillionschikov, Dmitri V.
dc.date2005-12-26
dc.date.accessioned2026-07-07T06:55:45Z
dc.date.available2026-07-07T06:55:45Z
dc.descriptionWe discuss some applications of the Morse-Novikov theory to some problems in modern physics, where appears a non-exact closed 1-form $ω$ (a multi-valued functional). We focus mainly our attention to the cohomology of the de Rham complex of a compact manifold $M^n$ with a deformed differential $d_ω=d +λω$. Using Witten's approach to the Morse theory one can estimate the number of critical points of $ω$ in terms of the cohomology of deformed de Rham complex with sufficiently large values of $λ$ (torsion-free Novikov's inequalities). We show that for an interesting class of solvmanifolds this cohomology can be computed as the cohomology of the corresponding Lie algebra $\mathfrak{g}$ associated with the one-dimensional representation $ρ_{λω}$.
dc.identifierhttps://arxiv.org/abs/math/0512572
dc.identifierhttp://arxiv.org/abs/math/0512572
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106386
dc.subjectAlgebraic Topology
dc.subjectMathematical Physics
dc.subject58A12; 17B30; 17B56; 57T15
dc.titleMultivalued functionals, one-forms and deformed de Rham complex
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