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...
متن کاملMorse Theory on Meshes
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 کاملOn Invariants of Morse Knots
We define and study Vassiliev invariants for (long) Morse knots. It is shown that there are Vassiliev invariants which can distinguish some topologically equivalent Morse knots. In particular, there is an invariant of order 3 for Morse knots with one maximum that distinguishes two different representations of the figure eight knot. We also present the results of computer calculations for some i...
متن کاملA Note on Morse Theory
Morse theory could be very well be called critical point theory. The idea is that by understanding the critical points of a smooth function on your manifold, you can recover the topology of your space. This basic idea has blossomed into many Morse theories. For instance, Robin Forman developed a combinatorial adaptation called discrete morse theory. We also have Morse-Bott theory, where we cons...
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ژورنال
عنوان ژورنال: Nature
سال: 1872
ISSN: 0028-0836,1476-4687
DOI: 10.1038/005444b0