In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions...

Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman. The theory has various practical applications in diverse...

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...

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...

K-theory Knot theory L-theory Lattice theory Lie theory M-theory Measure theory Model theory Morse theory Module theory Nevanlinna theory Number theory...

up morse in Wiktionary, the free dictionary. Morse may refer to: Morse (surname) Morse Goodman (1917-1993), Anglican Bishop of Calgary, Canada Morse Robb...

In mathematics, stratified Morse theory is an analogue to Morse theory for general stratified spaces, originally developed by Mark Goresky and Robert...

mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using...

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...

Measure theory — Model theory — Module theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — Order theory — PCF...

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...

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...

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...

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...

of manifolds arise naturally via Morse theory. The modification of handle structures is closely linked to Cerf theory. Consider the standard CW-decomposition...

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...

topological constructions, such as smooth surgery theory or the construction of cobordisms. Morse theory is an important tool which studies smooth manifolds...

intimately connected with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology...

In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold...

dahs. Morse code is named after Samuel Morse, one of the early developers of the system adopted for electrical telegraphy. International Morse code encodes...

pieces. Handlebodies play an important role in Morse theory, cobordism theory and the surgery theory of high-dimensional manifolds. Handles are used...

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...

geometry, discrete exterior calculus, discrete Morse theory, discrete optimization, discrete probability theory, discrete probability distribution, difference...

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...

invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology,...

use of some further simplifications. Perelman developed a version of Morse theory on Alexandrov spaces.[P93] Despite the lack of smoothness in Alexandrov...

topological degree theory, Jordan separation theorem, Lefschetz fixed-point theorem) Morse theory and Lusternik–Schnirelmann category theory methods of complex...

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...

partially ordered sets, decision trees, necklace problems and discrete Morse theory. It should not be confused with combinatorial topology which is an older...

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...