Homotopy
Homotopy An illustration of a homotopy between the two bold paths In topology ... other, such a deformation being called a homotopy between the two functions. An outstanding use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants ...
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Talk:Homotopy
Talk:Homotopy I think it is not true as ... article, that when X and Y are homotopy equivalent, and X is locally path connected ... Yes, locally path-connected isn't a homotopy invariant. It seems to me the stuff on homotopy groups belongs in its own article. -- ...
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User:Alodyne/Hopf invariant
User:Alodyne/Hopf invariant < User:Alodyne This is where the Hopf invariant page starts In algebraic topology, a branch of mathematics, the Hopf invariant is an number associated to a continuous ... 1(q) by Q. Then the Hopf invariant H(f) is defined as the linking ... integer. H(f) depends only on the homotopy class of f. A famous theorem ...
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Image:Homotopy between two paths.png
Image:Homotopy between two paths.png Image File history ... by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no ...
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List of mathematics articles (G-I)
... harmonic mean -- Geometric hashing -- Geometric integrator -- Geometric invariant theory -- Geometric kite -- Geometric mean -- Geometric model ... exploration algorithm -- Graph (functions) -- Graph homomorphism -- Graph invariant -- Graph isomorphism -- Graph labeling -- Graph manifold -- Graph ... Gröbner basis -- Gromov-Hausdorff convergence -- Gromov-Witten invariant -- Gromov's compactness theorem -- Gromov's theorem ... Hartogs' theorem -- Hash mark -- Hasse diagram -- Hasse invariant of a quadratic form -- Hasse–Minkowski theorem -- Hasse ... Homomorphism -- Homoscedasticity -- Homothetic transformation -- Homothety -- Homotopical algebra -- Homotopy -- Homotopy category of topological spaces -- Homotopy ...
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User:Mathbot/Changes mathlist
... Heterogeneous Added History of computer science Added Homotopy extension property Added International Mathematics Competition for ... element method in structural mechanics Added Fully invariant subgroup Added Growth curve Added H∞ Added ... space Added Carminati-McLenaghan invariants Added Curvature invariant (general relativity) Added Electrogravitic tensor Added Elongated ... Residue class-wise affine groups Added Stable homotopy category Added Subderivative Added Wandering salesman problem ... Added Bulgarian solitaire Added Duffing equation Added Invariant basis number Added Lambda abstraction Added ...
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Fundamental group
... point. The fundamental group is the first homotopy group. Intuition and definition Before giving a ... t). Such an h is called a homotopy from f to g, and the corresponding equivalence classes are called homotopy classes. The product f ∗ g of ... twice the speed. The product of two homotopy classes of loops [f] and [g] is ... With this product, the set of all homotopy classes of loops with base point ...
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Steenrod algebra
... object of great importance, most especially to homotopy theorists. More precisely, for a given prime ... p=2. The requirements of calculations of homotopy groups mean that homological algebra over the ... viewed as an approximation to the stable homotopy groups of spheres, objects of modern mathematics ... solutions by Frank Adams of the Hopf invariant one problem and the vector fields on ... gave a second solution of the Hopf invariant one problem, using operations in K- ...
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Topology glossary
... topology. The function H is called a homotopy (in Y) between f and g. Homotopy. See Homotopic maps. Hyper-connected. A space ... in X. Metric. See Metric space. Metric invariant. A metric invariant is a property which is preserved under ... Compare with locally simply connected; here, the homotopy is allowed to live in X, ...
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Floer homology
... mapping torus of the symplectomorphism. It is invariant under Hamiltonian isotopy of the symplectomorphism. It ... Floer homology This is a three-manifold invariant connected to Donaldson theory . It studies the ... a 3-manifold and whose differential counts invariant solutions to the Seiberg-Witten equations on ... Floer homology Heegaard Floer homology is an invariant of a closed 3-manifold equipped with ... on the homology groups, and the filtered homotopy type is a powerful knot invariant, ...
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