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Combinatorica, 2000
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1991
This chapter is the heart of the book. Quite a few spectacular theorems will be proved. The main ones are the famous convexity theorem of Atiyah [7] and Guillemin—Sternberg [63] which asserts that the image of a compact connected symplectic manifold under the momentum mapping of a Hamiltonian torus action is a convex polyhedron (this is Theorem ...
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This chapter is the heart of the book. Quite a few spectacular theorems will be proved. The main ones are the famous convexity theorem of Atiyah [7] and Guillemin—Sternberg [63] which asserts that the image of a compact connected symplectic manifold under the momentum mapping of a Hamiltonian torus action is a convex polyhedron (this is Theorem ...
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Morse Theory, Discrete Morse Theory and Applications
Theoretical and Natural ScienceBy employing a specific class of smooth functions to study a space, Morse theory establishes deep connections between analysis and topology. It is a classical subject of pure mathematics, originally pioneered by Marston Morse in the 1920s. In this article, we use Morse theory to present a proof of an interesting result on the knots, known as the Fáry ...
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Denoising with discrete Morse theory
The Visual Computer, 2021Denoising noisy datasets is a crucial task in this data-driven world. In this paper, we develop a persistence-guided discrete Morse theoretic denoising framework. We use our method to denoise point-clouds and to extract surfaces from noisy volumes. In addition, we show that our method generally outperforms standard methods.
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COMBINATORIAL NOVIKOV–MORSE THEORY
International Journal of Mathematics, 2002In [7, 8, 9], we developed a combinatorial Morse theory which can be applied to any CW complex. In [25, 26] Novikov presented a generalization of classical Morse theory in which the Morse function is replaced by a closed 1-forms. In this paper we extend our combinatorial Morse theory to include a combinatorial analog of Novikov's theory.
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On Some Results in Morse Theory
Canadian Journal of Mathematics, 1975The /z-cobordism theorem in [8], the generalized Poincaré conjecture in higher dimensions in [20] and several other results in differential topology are proved by using the following theorems of Morse theory:(1) the elimination of critical points;(2) the existence of nondegenerate functions for which the descending and ascending bowls have normal ...
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manuscripta mathematica, 1991
It is shown that the assignment of a cell-complex to a Morse function on a compact smooth manifold can be achieved uniquely up to a contractible space of parameters and continuously in an appropriate sense with respect to these parameters among which being the Riemannian metrics on the manifold.
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It is shown that the assignment of a cell-complex to a Morse function on a compact smooth manifold can be achieved uniquely up to a contractible space of parameters and continuously in an appropriate sense with respect to these parameters among which being the Riemannian metrics on the manifold.
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