nLab
clutching construction

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Topology

Contents

Idea

The clutching construction is the construction of a GG-principal bundle on an n-sphere from a cocycle in GG-Cech cohomology given by the covering of the nn-sphere by two semi-nn-spheres that overlap a bit at the equator, and one single transition function on that equator S n1GS^{n-1} \to G.

Applications

In physics

In physics, in gauge theory, the clutching construction plays a central role in the discussion of Yang-Mills instantons, and monopoles (Dirac monopole). Here the discussion is usually given in terms of gauge fields on nn-dimensional Minkowski spacetime such that they vanish at infinity. Equivalently this means that one has gauge fields on the one-point compactification of Minkowski spacetime, which is the n-sphere. The transition function of the clutching construction then appears as the asymptotic gauge transformation.

References

Reviews include

Revised on March 7, 2014 00:35:50 by Urs Schreiber (89.204.135.60)