homotopy group
81Stiefel manifold — In mathematics, the Stiefel manifold V k (R n ) is the set of all orthonormal k frames in R n . That is, it is the set of ordered k tuples of orthonormal vectors in R n . Likewise one can define the complex Stiefel manifold V k (C n ) of… …
82Whitehead product — The Whitehead product is a graded quasi Lie algebra structure on the homotopy groups of a space. It was defined by J. H. C. Whitehead in an Annals of Mathematics paper from 1941. Given elements f in pi k(X), g in pi l(X), the Whitehead bracket :… …
83Stiefel–Whitney class — In mathematics, the Stiefel–Whitney class arises as a type of characteristic class associated to real vector bundles E ightarrow X. It is denoted by w ( E ), taking values in H^*(X; /2), the cohomology groups with mod 2 coefficients. The… …
84Adams filtration — In mathematics, especially in the area of algebraic topology known as stable homotopy theory, the Adams filtration and the Adams Novikov filtration allow a stable homotopy group to be understood as built from layers, the n th layer containing… …
85't Hooft-Polyakov monopole — In theoretical physics, the t Hooft Polyakov monopole (hedgehog) is a topological soliton similar to the Dirac monopole but without any singularities. It arises in the case of a Yang Mills theory with a gauge group G, coupled to a Higgs field… …
86Induced homomorphism (algebraic topology) — In mathematics, especially in the area of topology known as algebraic topology, an induced homomorphism is a way of relating the algebraic invariants of topological spaces which are already related by a continuous function. Such homomorphism… …
87't Hooft–Polyakov monopole — In theoretical physics, the t Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without any singularities. It arises in the case of a Yang–Mills theory with a gauge group G, coupled to a Higgs field which… …
88Suspension (topology) — In topology, the suspension SX of a topological space X is the quotient space::SX = (X imes I)/{(x 1,0)sim(x 2,0)mbox{ and }(x 1,1)sim(x 2,1) mbox{ for all } x 1,x 2 in X}of the product of X with the unit interval I = [0, 1] . Intuitively, we… …
89Postnikov system — In homotopy theory, a branch of algebraic topology, a Postnikov system (or Postnikov tower) is a way of constructing a topological space from its homotopy groups. Postnikov systems were introduced, and named after, Mikhail Postnikov.The Postnikov …
90Rokhlin's theorem — In 4 dimensional topology, a branch of mathematics, Rokhlin s theorem states that if a smooth, compact 4 manifold M has a spin structure (or, equivalently, the second Stiefel Whitney class w 2( M ) vanishes), then the signature of its… …
