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Displaying 821 – 840 of 4977

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Cocycle invariants of codimension 2 embeddings of manifolds

Józef H. Przytycki, Witold Rosicki (2014)

Banach Center Publications

We consider the classical problem of a position of n-dimensional manifold Mⁿ in n + 2 . 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 M n + 2 . In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in n + 2 we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M . We show that if the fundamental group of each leaf of is isomorphic to Z , then is without holonomy. We also show that if π 2 ( M ) 0 and the fundamental group of each leaf of is isomorphic to Z k ( k Z 0 ), then is without holonomy.

Codimension two transcendental submanifolds of projective space

Wojciech Kucharz, Santiago R. Simanca (2010)

Annales de l’institut Fourier

We provide a simple characterization of codimension two submanifolds of n ( ) that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when n 6 . If the codimension two submanifold is a nonsingular algebraic subset of n ( ) whose Zariski closure in n ( ) is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in n ( ) .

Currently displaying 821 – 840 of 4977