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Displaying 821 –
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We consider the classical problem of a position of n-dimensional manifold Mⁿ in . We show that we can define the fundamental (n+1)-cycle and the shadow fundamental (n+2)-cycle for a fundamental quandle of a knotting . In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).
Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold . We show that if the fundamental group of each leaf of is isomorphic to , then is without holonomy. We also show that if and the fundamental group of each leaf of is isomorphic to (), then is without holonomy.
We provide a simple characterization of codimension two submanifolds of that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when . If the codimension two submanifold is a nonsingular algebraic subset of whose Zariski closure in is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in .
Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.
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