Une théorie catégorique d'homotopie simple
Let be a codim 1 local foliation generated by a germ of the form for some complex numbers and germs of holomorphic functions at the origin in . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for is equivalent to the unfolding theory for the multiform function...
The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.
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...
We prove a uniqueness result of weak solutions to the Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term.
We establish in this paper a lower bound for the volume of a unit vector field defined on , . This lower bound is related to the sum of the absolute values of the indices of at and .