mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology...

of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology. The...

are given over the space. Differential geometry is closely related to, and is sometimes taken to include, differential topology, which concerns itself with...

r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds. Contact geometry studies 1-forms that...

necessarily a discrete subspace of its domain X . {\displaystyle X.} In differential topology: Let M {\displaystyle M} and N {\displaystyle N} be smooth manifolds...

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...

may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a two-dimensional space; this...

have a number of nice properties and are an important concept in differential topology. Three special cases of constant rank maps occur. A constant rank...

branches of topology, including differential topology, geometric topology, and algebraic topology. The fundamental concepts in point-set topology are continuity...

fixed-point theorem (differential topology) Atiyah–Segal completion theorem (homotopy theory) Atiyah–Singer index theorem (elliptic differential operators, harmonic...

interpreted as infinitesimals Differential topology Differential (pushforward) The total derivative of a map between manifolds. Differential exponent, an exponent...

well as analysis, and spurred the development of algebraic and differential topology. Riemannian geometry was first put forward in generality by Bernhard...

specific to differential geometry and differential topology. The following three glossaries are closely related: Glossary of general topology Glossary of...

mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus...

that allows for differential calculus on the manifold. If M is already a topological manifold, it is required that the new topology be identical to the...

and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form...

areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric...

Frobenius theorem (differential topology) Distribution (differential geometry) integral curve foliation integrability conditions for differential systems Fiber...

Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about...

In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector...

(1990) Topology of 4-Manifolds. Princeton University Press. ISBN 0-691-08577-3. Guillemin, Victor and Pollack, Alan (1974) Differential Topology. Prentice-Hall...

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants...

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

February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems...

play a major role in setting up and solving partial differential equations. In differential topology, the exterior derivative and Lie derivative operators...

exterior derivative and the Lie derivative form a Lie superalgebra. In differential topology, a vector field may be defined as a derivation on the ring of smooth...

and multiplication by −i on the (0, 1)-vector fields. Just as we build differential forms out of exterior powers of the cotangent bundle, we can build exterior...

topology of Minkowski space". Topology. 6 (2): 161–170. doi:10.1016/0040-9383(67)90033-X. Penrose, Roger (1972), Techniques of Differential Topology in...

'topology is rubber-sheet geometry'. Subfields of topology include geometric topology, differential topology, algebraic topology and general topology....

A symplectic space may refer to: Symplectic manifold Symplectic vector space This disambiguation page lists articles associated with the title Symplectic...