Titlebook: Singularities and Foliations. Geometry, Topology and Applications; BMMS 2/NBMS 3, Salva Raimundo Nonato Araújo dos Santos,Aurélio Menegon

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Some Open Problems in Complex Singularitieson for complex singularities and the topology of analytic foliations near an isolated singularity. (iv) Rochlin’s signature theorem and Gorenstein surface singularities. (v) The index of a vector field on a singular variety. These are all topics on which I have been interested for a long time.

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A Brief Survey on Singularities of Geodesic Flows in Smooth Signature Changing Metrics on 2-Surfacesthere exists a unique geodesic passing through the point . with the direction .. On the contrary, geodesics cannot pass through a point . in arbitrary tangential directions, but only in some admissible directions; the number of admissible directions is 1 or 2 or 3. We study this phenomenon and the local properties of geodesics near ..

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Combinatorial Models in the Topological Classification of Singularities of Mappingsels which codify all the topological information of the map germ .. According to Fukuda’s work, the topology of such germs is determined by the link, which is obtained by taking the intersection of the image of . with a small enough sphere centered at the origin. If ., then the link is a topological

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A Brief Survey on Singularities of Geodesic Flows in Smooth Signature Changing Metrics on 2-Surfacesenerically, a pseudo-Riemannian metric on a 2-manifold . changes its signature (degenerates) along a curve ., which locally separates . into a Riemannian (.) and a Lorentzian (.) domain. The geodesic flow does not have singularities over . and ., and for any point . and every tangential direction .

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On Singular Holomorphic Foliations with Projective Transverse Structuresic situation is the case of a foliation with singularities . on a complex analytic space . of dimension two and the structure exists in the complement of some analytic subset . of codimension one. The main case occurs, as we shall see, when the analytic set is invariant by the foliation. We address

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Singular Fibers of Stable Maps of Manifold Pairs and Their Applicationsassify singular fibers of . stable maps of (., .) into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and obtain certain cobordism invariants for Morse functions on manifold pairs ., where . is a closed surface and . is a closed 1-dimensional

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Some Open Problems in Complex Singularitiesnks of an isolated singularity germ and the Zariski-Lipman conjecture; (ii) Graph manifolds and links of surface singularities. (iii) Milnor’s fibration for complex singularities and the topology of analytic foliations near an isolated singularity. (iv) Rochlin’s signature theorem and Gorenstein sur

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