nLab Spin(7)-instanton



The concept of Spin(7)Spin(7)-instantons (Lewis 98) is an analogue of that of Yang-Mills instantons for SU(2)-principal connections on 4-dimensional manifolds, to (8-dimensional) Spin(7) manifolds.


On a Spin(7) manifold the differential 2-forms decompose into two irreducible representations, Λ 7\Lambda_7 and Λ 21\Lambda_{21} under the action of Spin(7) (e.g. Lewis 98, p. 13).

A connection on the Spin(7)Spin(7)-manifold is called a Spin(7)Spin(7)-instanton it its curvature 2-form has vanishing component in the representation Λ 7\Lambda_7 (Lewis 98, def.3.1).


Last revised on January 22, 2016 at 16:48:28. See the history of this page for a list of all contributions to it.