mathematics, the geometric topology is a topology one can put on the set H of hyperbolic 3-manifolds of finite volume. Convergence in this topology is a crucial...

mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. Geometric topology as an...

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

The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way...

concerns the geometric properties of smooth manifolds, including notions of size, distance, and rigid shape. By comparison differential topology is concerned...

differential topology and geometric topology. For a list of terms specific to algebraic topology, see Glossary of algebraic topology. All spaces in this glossary...

{R} ^{n}} . The topologies do coincide in the case that each point in the complex lies only in finitely many simplices. Each geometric complex can be associated...

theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological...

mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries of solid objects in ordinary three-dimensional...

methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines...

knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be used to refer to the study of topological spaces of...

to the zero function. A linear graph has a natural topology that generalizes many of the geometric aspects of graphs with vertices and edges. Outer space...

parametrizing marked objects. In the 1970s and 1980s the theory developed interactions with symplectic geometry and equivariant topology, and was used to...

objects mathematically using the algebraic topology concept of cohomology. An early example of an impossible object comes from Apolinère Enameled, a 1916 advertisement...

1980s and early 1990s. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, algebraic topology, computational group...

mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are...

In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about...

wikidata descriptions as a fallback Subpaving – Geometrical object Willard, Stephen (1998). General Topology. Dover Publications. p. 104. ISBN 0-486-43479-6...

shipbuilders of 1960s. Geometric models can be built for objects of any dimension in any geometric space. Both 2D and 3D geometric models are extensively...

speaking, a topological space is a geometric object, and a homeomorphism results from a continuous deformation of the object into a new shape. Thus, a square...

(1976). Čech and Steenrod homotopy theories with applications to geometric topology. Lecture Notes in Maths. Vol. 542. Springer-Verlag. doi:10.1007/BFb0081083...

trace, and transfer", Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), PWN-Polish Scientific Publishers, pp. 81–102, ISBN 9788301017873...

Set-theoretic topology Set theory Sheaf theory The study of sheaves, which connect local and global properties of geometric objects. Sheaf cohomology...

geology and medical image processing. Geometric models are usually distinguished from procedural and object-oriented models, which define the shape...

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

algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from topologies that are commonly used...

algebraic topology. Category theory is used in almost all areas of mathematics. In particular, many constructions of new mathematical objects from previous...

figure/object to have more than one line of symmetry. The types of symmetries that are possible for a geometric object depend on the set of geometric transforms...

relationship between differential equations and topology. The following is a partial list of major topics within geometric analysis: Gauge theory Harmonic maps Kähler–Einstein...

In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of...