In mathematics, an isotopy from a possibly non-associative algebra A to another is a triple of bijective linear maps (a, b, c) such that if xy = z then...
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other Isotopy of quasigroups. See Quasigroup#Homotopy and isotopy. Isotopy of loops, a triple of maps with certain properties. Isotopy of an algebra, a triple...
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mathematical field of abstract algebra, isotopy is an equivalence relation used to classify the algebraic notion of loop. Isotopy for loops and quasigroups...
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Octonion (redirect from Dixon algebra)
an automorphism. The isotopy group of an algebra is the group of all isotopies, which contains the group of automorphisms as a subgroup. The isotopy group...
42 KB (5,316 words) - 02:52, 26 February 2025
Homotopy (redirect from Isotopy (topology))
to the definition of isotopy. An ambient isotopy, studied in this context, is an isotopy of the larger space, considered in light of its action on the...
24 KB (3,479 words) - 13:22, 17 July 2025
sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important...
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Small Latin squares and quasigroups (redirect from Isotopy class)
disjoint union of isotopy classes and an isotopy class is a disjoint union of isomorphism classes. Let (Q,∘) and (R,∗) be two quasigroups. An ordered triple...
26 KB (3,515 words) - 14:18, 15 January 2025
up to isotopy. To compose two planar tangles, put the output disk of one into an input of the other, having as many intervals, same shading of marked...
22 KB (3,081 words) - 14:54, 16 July 2025
Braid group (category Diagram algebras)
classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see § Introduction). Example applications of braid...
36 KB (4,920 words) - 11:36, 14 July 2025
Quasigroup (redirect from Loop (algebra))
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible...
32 KB (3,679 words) - 02:22, 19 July 2025
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...
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Symplectomorphism (redirect from Hamiltonian isotopy)
Hamiltonian vector fields coincide, so the notions of Hamiltonian isotopy and symplectic isotopy of symplectomorphisms coincide. It can be shown that the...
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glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category...
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John Milnor (category Members of the United States National Academy of Sciences)
dissertation, titled "Isotopy of links", also under the supervision of Fox. His dissertation concerned link groups (a generalization of the classical knot...
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class group – Group of isotopy classes of a topological automorphism group Permutation group – Group whose operation is composition of permutations Regular...
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called an isotopy. If the three maps of an isotopy are in S O ( 8 ) {\displaystyle \operatorname {SO(8)} } , the isotopy is called an orthogonal isotopy. If...
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Etta Zuber Falconer (category University of Wisconsin–Madison College of Letters and Science alumni)
invariant under isotopy (PhD). Emory University. Etta Zuber Falconer at the Mathematics Genealogy Project Falconer, Etta (1970). "Isotopy invariants in...
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(Jordan algebra) in mathematics, a method of modifying the product on a Jordan algebra An isotope of an algebra: see Isotopy of algebras An isotope of a loop...
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René Thom (category Recipients of the National Order of Scientific Merit (Brazil))
developed the theory of stratified sets and stratified maps, proving a basic stratified isotopy theorem describing the local conical structure of Whitney stratified...
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a solution to the special Lagrangian equation inside a Hamiltonian isotopy class of Lagrangian submanifolds. In particular the conjecture contains two...
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Knot invariant (redirect from Isotopy invariant)
equivalence is often given by ambient isotopy but can be given by homeomorphism. Some invariants are indeed numbers (algebraic), but invariants can range from...
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Knot theory (redirect from Algebraic topology based on knots)
deformation of R 3 {\displaystyle \mathbb {R} ^{3}} upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted...
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Tropical geometry (redirect from Tropical algebraic geometry)
The group law of the cubics. Oleg Viro used tropical curves to classify real curves of degree 7 in the plane up to isotopy. His method of patchworking...
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invertible this is referred to as an isotope. A homotope of a Jordan algebra is again a Jordan algebra: isotopy defines an equivalence relation. If y is nuclear...
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3-manifolds have a unique (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the 3-manifold obtained by...
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Regular (section Algebra and number theory)
chains in computer algebra Regular element (disambiguation), certain kinds of elements of an algebraic structure Regular extension of fields Regular ideal...
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Tangle (mathematics) (redirect from Algebraic tangle)
n-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. Tangle theory can be considered...
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In mathematics, especially in differential topology, Thom's first isotopy lemma states: given a smooth map f : M → N {\displaystyle f:M\to N} between...
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Latin square (category Non-associative algebra)
1, 2, 3 or 6 isotopy classes. The number of structurally distinct Latin squares (i.e. the squares cannot be made identical by means of rotation, reflection...
32 KB (3,884 words) - 03:05, 14 July 2025
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the...
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