Morse theory


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Morse theory

[′mȯrs ‚thē·ə·rē]
(mathematics)
The study of differentiable mappings of differentiable manifolds, which by examining critical points shows how manifolds can be constructed from one another.
References in periodicals archive ?
Writing in the area of differential geometry at the graduate level, Moore gives foundations for a partial Morse theory of minimal surfaces in Riemannian manifolds.
To this end, we need to mildly generalize some elements of Discrete Morse Theory in order to be able to work with nonregular CW-complexes or, correspondingly, face categories that are not posets (see Section 5.
Our approach combines variational techniques based on the critical point theory, together with Morse theory.
The topics include some algebraic methods in semi-Markov chains, statistical topology through Morse theory persistence and non-parametric estimation, structural properties of the generalized Dirichlet distributions, projections on invariant subspaces, combining statistical models, regular fractions and indicator polynomials, and some hypothesis tests for Wishart models on symmetric cones.
Under Phase I of the NSF grant, Raindrop Geomagic used Morse Theory research to create a structured representation of a computer model by distinguishing between flat and highly curved feature surfaces.
Knudson bases his introduction to Morse theory on John Milnor's Morse Theory and Yukio Matsumoto's An Introduction to Morse Theory, both of which he considers elegant masterpieces.
The proof follows the same outline as the previous study except that we use discrete Morse theory to determine the homotopy type of the associated complexes of ordered set partitions.
The authors work with a new sequence of eigenvalues that employs the cohomological index to systematically develop alternative tools such as nonlinear linking and local splitting theories to apply Morse theory to quasilinear problems.
2 is closely related to results of Jollenbeck-Welker, of Skoldberg, and of Kozlov (see (3), (8), and (4)) developing algebraic versions of discrete Morse theory.
They then move briskly through Toponogov's theorem, homogeneous spaces, Morse theory, closed deodesics and the cut locus, the sphere theorem and its generalizations, the differentiable space theorem, complete manifolds of non-negative curvature, and compact manifolds of non-positive curvature.
Other topics include automated reverse engineering of free form objects using Morse theory, dense depth and color acquisition of repetitive motions, examplar-based shape from shading, and generalized MPU implicits using belief propagation.
Some 60 years later Novikov, who was working on a problem in hydrodynamics, formulated a circle-based Morse theory.