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" The coward's guide to conflict : "
Tim Ursiny.
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Latin Dissertation
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| Language of Document
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English
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| Record Number
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1105910
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TLpq2346618086
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| Main Entry
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Islam, Md Shariful
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Richardson, Ken
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| Title & Author
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Leafwise Morse-Novikov Cohomological Invariants of Foliations\ Islam, Md SharifulRichardson, Ken
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| College
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Texas Christian University
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| Date
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2019
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| student score
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2019
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| Degree
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Ph.D.
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| Page No
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95
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| Abstract
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The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential d_ω=d+ω∧ , where ω is a closed 1-form. We study Morse-Novikov cohomology in the context of singular distributions given by the kernel of differential forms, and foliations of manifold. The kernel of a d_ω closed form is involutive and hence gives a foliation of a manifold. A transversely oriented foliation of a Riemannian manifold uniquely determines leafwise Morse-Novikov cohomology groups, which are independent of the choice of metric in the sense that different metrics correspond to isomorphic groups. The relevant 1-form ω, which is always leafwise closed, can be chosen to be the mean curvature 1-form of the transverse distribution of the foliation. In the case of Riemannian foliations, we prove that the reduced leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and Poincar´e duality. We also show that for general singular foliations, the isomorphism classes of the induced leafwise Morse-Novikov cohomology groups are foliated homotopy invariants.
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Mathematics
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