Page 1

Displaying 1 – 9 of 9

Showing per page

Bernstein-Sato Polynomials and Spectral Numbers

Andréa G. Guimarães, Abramo Hefez (2007)

Annales de l’institut Fourier

In this paper we will describe a set of roots of the Bernstein-Sato polynomial associated to a germ of complex analytic function in several variables, with an isolated critical point at the origin, that may be obtained by only knowing the spectral numbers of the germ. This will also give us a set of common roots of the Bernstein-Sato polynomials associated to the members of a μ -constant family of germs of functions. An example will show that this set may sometimes consist of all common roots.

Close cohomologous Morse forms with compact leaves

Irina Gelbukh (2013)

Czechoslovak Mathematical Journal

We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave γ , then any close cohomologous form has a compact leave close to γ . Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease...

Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity

Magdalena Zielenkiewicz (2014)

Open Mathematics

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of...

On the structure of a Morse form foliation

I. Gelbukh (2009)

Czechoslovak Mathematical Journal

The foliation of a Morse form ω on a closed manifold M is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of M and ω . Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω . The set of the ranks of all forms defining a given foliation without minimal...

Quadratic mappings and configuration spaces

Gia Giorgadze (2003)

Banach Center Publications

We discuss some approaches to the topological study of real quadratic mappings. Two effective methods of computing the Euler characteristics of fibers are presented which enable one to obtain comprehensive results for quadratic mappings with two-dimensional fibers. As an illustration we obtain a complete topological classification of configuration spaces of planar pentagons.

Real deformations and invariants of map-germs

J. H. Rieger, M. A. S. Ruas, R. Wik Atique (2008)

Banach Center Publications

A stable deformation f t of a real map-germ f : , 0 p , 0 is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification f t are real. A related notion is that of a good real perturbation f t of f (studied e.g. by Mond and his coworkers) for which the homology of the image (for n < p) or discriminant (for n ≥ p) of f t coincides with that of f C t . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good real perturbation....

Topological invariants of isolated complete intersection curve singularities

V. H. Jorge Pérez, M. E. Hernandes (2009)

Czechoslovak Mathematical Journal

In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

Currently displaying 1 – 9 of 9

Page 1