Suppose that X is a topological space, f is a real valued function on X, and c is a real
number. Then we will denote by X≤ c the subspace of points x in X such that f (x)≤ c. The …

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a
singular space into smooth manifolds, a great geometrical idea due to R. Thom and H …

Abstract Donaldson–Thomas invariants $ DT^\alpha (\tau) $ are integers which 'count'$\tau
$-stable coherent sheaves with Chern character $\alpha $ on a Calabi–Yau 3-fold $ X …

A basic problem in algebraic geometry is to extract geometrical information from the
algebraic equations which define an algebraic variety. Many tools have been created to …

Vector fields on manifolds play a major role in mathematics and other sciences. In particular,
the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold …

In recent years, intersection homology and perverse sheaves have become indispensable
tools for studying the topology of singular spaces. This book provides a gentle introduction to …

LET (X, 0) be an isolated complex analytic surface singularity which is reduced and
irreducible. This paper is concerned with certain necessary conditions (X, 0) must satisfy in …

This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this book
is to give an overview of selected topics on the topology of real and complex isolated …

In this paper we discuss the topology of the image of a stable perturbation of a finitely
determined map-germ fo:(~ n. 0)....(~ n+ 1.0). and its relation to the number of parameters …

Milnor's fibration theorem is about the geometry and topology of real and complex analytic
maps near their critical points, a ubiquitous theme in mathematics. As such, after 50 years …