String group

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In topology, a branch of mathematics, a string group is an infinite-dimensional group String(n) introduced by Stolz (1996) as a 3-connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in addition to being able to define holonomy along paths, one can also define holonomies for surfaces going between strings.

There is a short exact sequence of topological groups

0\rightarrow K(Z,2)\rightarrow \text{String}(n)\rightarrow \text{Spin}(n)\rightarrow 0

where K(Z, 2) is an Eilenberg–MacLane space and Spin(n) is a spin group.


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