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...

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...

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

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...

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...

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

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

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...

coverage or topology or geometric modality. They were introduced by William Lawvere (1971) and Myles Tierney. If E is a topos, then a topology on E is a...

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

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...

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

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

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...

algebraic topology on the set of discrete, faithful representations of a Kleinian group into PSL(2,C). Another topology, the geometric topology (also called...

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

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

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

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...

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

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

\chi =2-2g-b} . In layman's terms, the genus is the number of "holes" an object has ("holes" interpreted in the sense of doughnut holes; a hollow sphere...

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

network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e., the nodes are...