Homotopy types of Spin^c(n)-gauge groups over S⁴

2021/07/13 by Simon Rea, Rea, Simon
Mathematics · Medicine · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2107.06000

Abstract

The gauge group of a principal G-bundle P over a space X is the group of G-equivariant homeomorphisms of P that cover the identity on X. We consider the gauge groups of bundles over S⁴ with Spin^c(n), the complex spin group, as structure group and show how the study of their homotopy types reduces to that of Spin(n)-gauge groups over S⁴. We then advance on what is known by providing a partial classification for Spin(7)- and Spin(8)-gauge groups over S⁴.

Citations

• The homotopy types of Sp(2)-gauge groups over closed, simply-connected four-manifolds

Related

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• Homotopy types of gauge groups related to S³-bundles over S⁴
• Homotopy types of SU(n)-gauge groups over non-spin 4-manifolds
• The homotopy types of Sp(2)-gauge groups over closed, simply-connected four-manifolds
• Odd primary homotopy types of the gauge groups of exceptional Lie groups