topology of manifolds
1Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …
2topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …
3Differential topology — In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.… …
4Classification of manifolds — In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Contents 1 Main themes 1.1 Overview 1.2 Different categories and additional… …
5Computational topology — Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its …
6List of geometric topology topics — This is a list of geometric topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of algebraic topology topics Publications in topology Contents 1 Low dimensional topology 1.1 …
7Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …
8Triangulation (topology) — In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K , homeomorphic to X , together with a homeomorphism h : K o X . Triangulation is… …
9Categories of manifolds — In mathematics, specifically geometry and topology, there are many different notions of manifold, with more or less structure, and corresponding notions of map between manifolds , each of which yields a different category and its own… …
10Low-dimensional topology — In mathematics, low dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3 manifolds and 4 manifolds, knot theory, and braid groups. It can be… …
