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Let $Ω \subset ℝ^{n}$ be a compact semianalytic set and let $ℱ$ be a collection of real analytic functions defined in some neighbourhood of $Ω$ . Let $Y_{ω}$ be the germ at $ω$ of the set $⋂_{f \in ℱ} f^{- 1} (0)$ . Then there exist analytic functions $v_{1}, v_{2}, ..., v_{s}$ defined in a neighbourhood of $Ω$ such that $\frac{1}{2} χ (lk (ω, Y_{ω})) = \sum_{i = 1}^{s} sgn v_{i} (ω)$ , for all $ω \in Ω$ .

Topological Invariants of Real Algebraic Curves

Benedict H. Gross (1980/1981)

Séminaire de théorie des nombres de Grenoble

Topological methods in representation theory.

Vilonen, Kari (1998)

Documenta Mathematica

Topological Order Complexes and Resolutions of Discriminant Sets

V. A. Vassiliev (1999)

Publications de l'Institut Mathématique

Topological order complexes and resolutions of discriminant sets.

Vassiliev, V.A. (1999)

Publications de l'Institut Mathématique. Nouvelle Série

Topological properties of certain incomplete regular intersections

Н.Ю. Нецветаев (1984)

Zapiski naucnych seminarov Leningradskogo

Topological triviality of versal unfoldings of complete intersections

James Damon (1984)

Annales de l'institut Fourier

We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in $C^{4}$ which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities.The algebraic conditions are related to the operation of adjoining powers,...

Topological types of fewnomials

Michel Coste (1998)

Banach Center Publications

Topological Types of p-Hyperelliptic Real Algebraic Curves.

E. Bujalance, J.J. Etayo, J.M. Gamboa (1987)

Mathematische Zeitschrift

Topological types of symmetries of elliptic-hyperelliptic Riemann surfaces and an application to moduli spaces.

José A. Bujalance, Antonio F. Costa, Ana M. Porto (2003)

RACSAM

Sea X una superficie de Riemann de género g. Diremos que la superficie X es elíptica-hiperelíptica si admite una involución conforme h de modo que X/〈h〉 tenga género uno. La involución h se llama entonces involución elíptica-hiperelíptica. Si g > 5 entonces la involución h es única, ver [1]. Llamamos simetría a toda involución anticonforme de X. Sea Aut±(X) el grupo de automorfismos conformes y anticonformes de X y σ, τ dos simetrías de X con puntos fijos y tales que {σ, hσ} y {τ, hτ} no...

Topologie comparée d'une courbe polaire et de sa courbe descriminante.

Hélène Maugendre (1999)

Revista Matemática Complutense

Let f be an analytic function germ at 0 in C2. We compare the topological complexity of the discriminant curve of f to the one of its polar curve.

Topologie des fonctions régulières et cycles évanescents.

Thomas Brélivet (2003)

Revista Matemática Complutense

One has two notions of vanishing cycles: the Deligne's general notion and a concrete one used recently in the study of polynomial functions. We compare these two notions which gives us in particular a relative connectivity result. We finish with an example of vanishing cycle calculation which shows the difficulty of a good choice of compactification.

Topologie d'un polynôme de deux variables complexes au voisinage de l'infini

Laurence Fourrier (1996)

Annales de l'institut Fourier

Nous donnons un système complet d’invariants de la classe de conjugaison topologique de polynômes de $ℂ^{2}$ en dehors d’un compact suffisamment grand dans les deux sens suivants : en tant que feuilletages (en oubliant les valeurs des fibres) et en tant que fonctions. Ces invariants sont donnés par un arbre pondéré, fléché et coloré, obtenu à partir de la résolution des singularités du polynôme sur la droite à l’infini. Nous donnons un critère de régularité pour les valeurs d’un polynôme et une description...

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Topological and Algebraic Cycles in Kuga-Shimura Varieties.

Topological Classification of 4-Dimensional Complete Intersections.

Topological dimensions for $u$ -groups.

Topological equisingularity for isolated complete intersection singularities

Topological invariants of analytic sets associated with Noetherian families