In 1895 Henri Poincaré published his topological work 'Analysis Situs'. A new subdiscipline in mathematics was born. Analysis Situs was an inspiration to new fields like algebraic topology, Morse theory and cobordism. With use of today’s knowledge and notation, Dirk Siersma views back to this histor
We initiate a classification of polynomials f : Cn - C of degree d having the top Betti number of the general fibre close to the maximum. We find a range in which the polynomial must have isolated singularities and another range where it may have at most one line singularity of Morse transversal typ
It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open po
Het weten in de wetenschap heeft wel iets te maken met het weten waarover hier geschreven wordt, het gaat over de betrekkelijkheid van de tijdschaal. Ik zag de drang waarmee de bomen zich uit de aarde wrongen, de tremor van de zee. Dit weten lijkt eenvoudig, het kennen van het fenomeen van de versne
We describe the structure of minimal round functions on closed surfaces and three-folds. The minimal possible number of critical loops is determined and typical non-equisingular round function germs are interpreted in the spirit of isolated line singularities. We also discuss a version of Lusternik-
We study vanishing cycles of meromorphic functions This gives a new and unitary point of view extending the study of the topology of holomorphic germs as initiated by Milnor in the sixties and of the global topology of polynomial functions which has been advanced more recently We dene singularitie
This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane established by Siersma In the present case a conflict surface arises equidistant from the given convex sets The Gaussian Mean Curvatures and the location of Umbilic Points o
This paper studies the smoothness and the curvature of conict sets of the distance function in the plane Conict sets are also well known as bisectors We prove smoothness in the case of two convex sets and give a formula for the curvature We generalize moreover to weighted distance functions the soca
Let f C n C be any polynomial function By using global polar methods we introduce models for the bers of f and we study the monodromy at atypical values of f including the value innity We construct a geometric monodromy with controlled behavior and dene global relative monodromy with respect to a
Lines on hypersurfaces with isolated singularities are classied New normal forms of simple singularities with respect to lines are obtained Several invariants are introduced
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