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Unfoldings of foliations with multiform first integrals

Tatsuo Suwa (1983)

Annales de l'institut Fourier

Let F = ( ω ) be a codim 1 local foliation generated by a germ ω of the form ω = f 1 ... f p i = 1 p λ i d f i f i for some complex numbers λ i and germs f i of holomorphic functions at the origin in C n . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of F . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for F is equivalent to the unfolding theory for the multiform function...

Unfoldings of holomorphic foliations.

Xavier Gómez-Mont (1989)

Publicacions Matemàtiques

The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.

Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion

Anna Beliakova, Christian Blanchet, Thang T. Q. Lê (2008)

Fundamenta Mathematicae

For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of...

Unit vector fields on antipodally punctured spheres: big index, big volume

Fabiano G. B. Brito, Pablo M. Chacón, David L. Johnson (2008)

Bulletin de la Société Mathématique de France

We establish in this paper a lower bound for the volume of a unit vector field v defined on 𝐒 n { ± x } , n = 2 , 3 . This lower bound is related to the sum of the absolute values of the indices of v at x and - x .

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