Category: Topology of Lie groups

Metaplectic group
In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an a
Spin group
In mathematics the spin group Spin(n) is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2) As a Lie group, Spi
Kuiper's theorem
In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible boun
Bott periodicity theorem
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott , which proved to be of foundational significance for much fur
Plate trick
In mathematics and physics, the plate trick, also known as Dirac's string trick, the belt trick, or the Balinese cup trick, is any of several demonstrations of the idea that rotating an object with st
J-homomorphism
In mathematics, the J-homomorphism is a mapping from the homotopy groups of the special orthogonal groups to the homotopy groups of spheres. It was defined by George W. Whitehead, extending a construc
P-compact group
In mathematics, in particular algebraic topology, a p-compact group is a homotopical version of a compact Lie group, but with all the local structure concentrated at a single prime p. This concept was
Orientation entanglement
In mathematics and physics, the notion of orientation entanglement is sometimes used to develop intuition relating to the geometry of spinors or alternatively as a concrete realization of the failure