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Magnetic monopole — It is impossible to make magnetic monopoles from a bar magnet. If a bar magnet is cut in half, it is not the case that one half has the north pole and the other half has the south pole. Inst … Wikipedia
Singular homology — In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of a… … Wikipedia
Van Kampen diagram — In the mathematical area of geometric group theory, a van Kampen diagram is a planar diagram used to represent the fact that a particular word among the generators of a group given by a group presentation represents the identity element in that… … Wikipedia
Topological defect — Also see base concepts: topology, differential equations, quantum theory condensed matter physics .In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a… … Wikipedia
Plane (geometry) — Two intersecting planes in three dimensional space In mathematics, a plane is a flat, two dimensional surface. A plane is the two dimensional analogue of a point (zero dimensions), a line (one dimension) and a space (three dimensions). Planes can … Wikipedia
Whitehead theorem — In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between topological spaces X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence provided X and Y are… … Wikipedia
'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… … Wikipedia
Skyrmion — In theoretical physics, a skyrmion, conceived by Tony Skyrme, is a mathematical model used to model baryons (a subatomic particle).A skyrmion is a homotopically non trivial classical solution of a nonlinear sigma model with a non trivial target… … Wikipedia
Vacuum manifold — In quantum field theory, the vacuum state may be degenerate. Each pure vacuum state generates its own superselection sector. The space of all pure vacuum states often has a manifold structure and is called the vacuum manifold.Vacuum manifolds… … Wikipedia
Circle bundle — In mathematics, an (oriented) circle bundle is an oriented fiber bundle where the fiber is the circle , or, more precisely, a principal U(1) bundle. It is homotopically equivalent to a complex line bundle. In physics, circle bundles are the… … Wikipedia
