منابع مشابه
Stratified Morse Theory in Arrangements
This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement. This is used to show that the complement of a complex hyperplane arrangement admits a minimal cell decomposition. Next we review the construction of a cochain complex whose cohomology computes the local system cohom...
متن کاملStratified Morse Theory: Past and Present
In 1974, Mark Goresky and Robert MacPherson began their development of intersection homology theory (see [24] in these volumes), and their first paper on this topic appeared in 1980; see [12]. At that time, they were missing a fundamental tool which was available for the study of smooth manifolds; they had no Morse Theory for stratified spaces. Goresky and MacPherson wished to have a Stratified...
متن کاملDiscrete Stratified Morse Theory: A User's Guide
Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and MacPherson [17]. We describe the basics of this theory and prove fundamental theorems relating the topology of a general simplicial complex with the critical simplice...
متن کاملGradient-Like Flows and Self-Indexing in Stratified Morse Theory
We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of gradientlike vector fields satisfying certain “stratified dimension bounds up to fuzz” for the ascending and descending sets. As a global consequence of this, we derive...
متن کاملEdge Flows: Stratified Morse Theory for Simple, Correct Isosurface Extraction
We present a method to characterize the topology of the level sets of trilinearly interpolated scalar fields. Our characterization is based on Morse theory, and in particular a variant called Stratified Morse theory capable of treating the piecewise-smooth aspect of trilinear interpolation. Algorithms such as Marching Cubes generate approximations to these level sets to a varying degree of fide...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1989
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1989-15813-8