In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions...
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Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman. The theory has various practical applications in diverse...
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topology now known as Morse theory. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite...
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foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system...
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K-theory Knot theory L-theory Lattice theory Lie theory M-theory Measure theory Model theory Morse theory Module theory Nevanlinna theory Number theory...
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up morse in Wiktionary, the free dictionary. Morse may refer to: Morse (surname) Morse Goodman (1917-1993), Anglican Bishop of Calgary, Canada Morse Robb...
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In mathematics, stratified Morse theory is an analogue to Morse theory for general stratified spaces, originally developed by Mark Goresky and Robert...
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mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using...
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Symplectic manifold (section Example: Morse theory)
branes. Another useful class of Lagrangian submanifolds occur in Morse theory. Given a Morse function f : M → R {\displaystyle f:M\to \mathbb {R} } and for...
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Measure theory — Model theory — Module theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — Order theory — PCF...
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In mathematics, digital Morse theory is a digital adaptation of continuum Morse theory for scalar volume data. The term was first promulgated by DB Karron...
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Anthony Perry Morse (21 August 1911 – 6 March 1984) was an American mathematician who worked in both analysis, especially measure theory, and in the foundations...
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invariants of the manifold are known. A relatively easy argument using Morse theory shows that a manifold can be obtained from another one by a sequence...
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In dynamical systems theory, an area of pure mathematics, a Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely...
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of manifolds arise naturally via Morse theory. The modification of handle structures is closely linked to Cerf theory. Consider the standard CW-decomposition...
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Hessian matrix (category Morse theory)
a saddle point). However, more can be said from the point of view of Morse theory. The second-derivative test for functions of one and two variables is...
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topological constructions, such as smooth surgery theory or the construction of cobordisms. Morse theory is an important tool which studies smooth manifolds...
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Cobordism (redirect from Cobordism theory)
intimately connected with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology...
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In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold...
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dahs. Morse code is named after Samuel Morse, one of the early developers of the system adopted for electrical telegraphy. International Morse code encodes...
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Handlebody (category Surgery theory)
pieces. Handlebodies play an important role in Morse theory, cobordism theory and the surgery theory of high-dimensional manifolds. Handles are used...
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higher dimensions by Solomon Lefschetz (1924). It is a complex analog of Morse theory that studies the topology of a real manifold by looking at the critical...
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Discrete mathematics (section Information theory)
geometry, discrete exterior calculus, discrete Morse theory, discrete optimization, discrete probability theory, discrete probability distribution, difference...
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In mathematics, the Morse–Palais lemma is a result in the calculus of variations and theory of Hilbert spaces. Roughly speaking, it states that a smooth...
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Floer homology (redirect from Seiberg–Witten Floer theory)
invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology,...
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use of some further simplifications. Perelman developed a version of Morse theory on Alexandrov spaces.[P93] Despite the lack of smoothness in Alexandrov...
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topological degree theory, Jordan separation theorem, Lefschetz fixed-point theorem) Morse theory and Lusternik–Schnirelmann category theory methods of complex...
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Novikov ring (category Morse theory)
by Sergei Novikov in the papers that initiated the generalization of Morse theory using a closed one-form instead of a function. The notion is used in...
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Combinatorics (redirect from Combinatorial theory)
partially ordered sets, decision trees, necklace problems and discrete Morse theory. It should not be confused with combinatorial topology which is an older...
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Edward Witten (section M-theory)
supergravity theory to simplify the argument. A third area mentioned in Atiyah's address is Witten's work relating supersymmetry and Morse theory, a branch...
35 KB (3,123 words) - 19:06, 13 September 2024