Lectures on Morse theory, old and new
نویسندگان
چکیده
منابع مشابه
Morse Theory on Graphs
Let Γ be a finite d-valent graph and G an n-dimensional torus. An " action " of G on Γ is defined by a map which assigns to each oriented edge, e, of Γ, a one-dimensional representation of G (or, alternatively, a weight, αe, in the weight lattice of G. For the assignment, e → αe, to be a schematic description of a " G-action " , these weights have to satisfy certain compatibility conditions: th...
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In this report, we discuss two papers that deal with computing Morse function on triangulated manifolds. Axen [1] gives an algorithm for computing Morse function on a triangulated manifold of arbitrary dimension but it not practical because of its space requirement. Hence, he describes an algorithm for computing critical points and their Morse indices for a 2-manifold. Edelsbrunner et al. [2] d...
متن کاملMorse theory on grassmanians
In the paper [N], while studying adiabatic deformations of Dirac operators on manifolds with boundary, we were led to the following nite dimensional dynamics problem. Consider (n) the grassmannian of lagrangian subspaces in the canonical symplectic space E = R2n . If A : E ! E is a selfadjoint operator anticommuting with the canonical complex structure J on E, then A belongs to the Lie algebra ...
متن کاملLectures on Nevanlinna theory
Value distribution of a rational function f is controlled by its degree d, which is the number of preimages of a generic point. If we denote by n(a) the number of solutions of the equation f(z) = a, counting multiplicity, in the complex plane C, then n(a) ≤ d for all a ∈ C with equality for all a with one exception, namely a = f(∞). The number of critical points of f in C, counting multiplicity...
متن کاملLectures on Dimension Theory
Preliminaries In this lecture, we give a quick review of the basics of classical commutative algebra. The following notation and terminology is used throughout. By a ring we mean a commutative ring with identity. For sets I, J, we write I ⊆ J to denote that I is a subset of J and I ⊂ J to denote that I is a proper subset of J, i.e., I ⊆ J and I = J. We denote the set of nonnegative integers by ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1982
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1982-15038-8