Faster access than browser!
32 relations: Braid, Braid group, Braid theory, Braided monoidal category, Cartesian product, Change ringing software, Chaotic mixing, Configuration space (mathematics), Fluid mechanics, Fundamental group, Geometry, Group (mathematics), Group action, Homotopy group, James Waddell Alexander II, Jones polynomial, Knot (mathematics), Knot theory, Link (knot theory), Manifold, Markov theorem, Nielsen–Thurston classification, Presentation of a group, Seifert fiber space, Symmetric group, Symmetric product (topology), Theory, Topological entropy, Topology, Topology and Its Applications, Up to, Vaughan Jones.
Braid
A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing three or more strands of flexible material such as textile yarns, wire, or hair.
New!!: Braid theory and Braid · See more »
Braid group
In mathematics, the braid group on strands (denoted), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see); and in monodromy invariants of algebraic geometry.
New!!: Braid theory and Braid group · See more »
Braid theory
In topology, a branch of mathematics, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalizations.
New!!: Braid theory and Braid theory · See more »
Braided monoidal category
In mathematics, a commutativity constraint \gamma on a monoidal category \mathcal is a choice of isomorphism \gamma_: A\otimes B \rightarrow B\otimes A for each pair of objects A and B which form a "natural family." In particular, to have a commutativity constraint, one must have A \otimes B \cong B \otimes A for all pairs of objects A,B \in \mathcal.
New!!: Braid theory and Braided monoidal category · See more »
Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
New!!: Braid theory and Cartesian product · See more »
Change ringing software
Change ringing software encompasses the several different types of software in use today in connection with change ringing.
New!!: Braid theory and Change ringing software · See more »
Chaotic mixing
In chaos theory and fluid dynamics, chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow.
New!!: Braid theory and Chaotic mixing · See more »
Configuration space (mathematics)
T^3/S_3, is the above orbifold. --> In mathematics, a configuration space (also known as Fadell's configuration space) is a construction closely related to state spaces or phase spaces in physics.
New!!: Braid theory and Configuration space (mathematics) · See more »
Fluid mechanics
Fluid mechanics is a branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
New!!: Braid theory and Fluid mechanics · See more »
Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
New!!: Braid theory and Fundamental group · See more »
Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
New!!: Braid theory and Geometry · See more »
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
New!!: Braid theory and Group (mathematics) · See more »
Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
New!!: Braid theory and Group action · See more »
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.
New!!: Braid theory and Homotopy group · See more »
James Waddell Alexander II
James Waddell Alexander II (September 19, 1888 September 23, 1971) was a mathematician and topologist of the pre-World War II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others.
New!!: Braid theory and James Waddell Alexander II · See more »
Jones polynomial
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.
New!!: Braid theory and Jones polynomial · See more »
Knot (mathematics)
In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).
New!!: Braid theory and Knot (mathematics) · See more »
Knot theory
In topology, knot theory is the study of mathematical knots.
New!!: Braid theory and Knot theory · See more »
Link (knot theory)
In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.
New!!: Braid theory and Link (knot theory) · See more »
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
New!!: Braid theory and Manifold · See more »
Markov theorem
In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures which are equivalent links.
New!!: Braid theory and Markov theorem · See more »
Nielsen–Thurston classification
In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface.
New!!: Braid theory and Nielsen–Thurston classification · See more »
Presentation of a group
In mathematics, one method of defining a group is by a presentation.
New!!: Braid theory and Presentation of a group · See more »
Seifert fiber space
A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles.
New!!: Braid theory and Seifert fiber space · See more »
Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
New!!: Braid theory and Symmetric group · See more »
Symmetric product (topology)
In algebraic topology, the symmetric product of a topological space consists of unordered -tuples of distinct points in.
New!!: Braid theory and Symmetric product (topology) · See more »
Theory
A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking.
New!!: Braid theory and Theory · See more »
Topological entropy
In mathematics, the topological entropy of a topological dynamical system is a nonnegative extended real number that is a measure of the complexity of the system.
New!!: Braid theory and Topological entropy · See more »
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
New!!: Braid theory and Topology · See more »
Topology and Its Applications
Topology and Its Applications is a peer-reviewed mathematics journal publishing research on topology.
New!!: Braid theory and Topology and Its Applications · See more »
Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
New!!: Braid theory and Up to · See more »
Vaughan Jones
Sir Vaughan Frederick Randal Jones (born 31 December 1952) is a New Zealand and American mathematician, known for his work on von Neumann algebras and knot polynomials.
New!!: Braid theory and Vaughan Jones · See more »
Redirects here:
Braid (mathematics), Braid index, Braid length, Braid number, Closed braid, Closed braids.
References
[1] https://en.wikipedia.org/wiki/Braid_theory
