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# The Classification of $\Pin_4$-Bundles over a $4$-Complex

Published:1999-06-01
Printed: Jun 1999
• Christian Weber
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## Abstract

In this paper we show that the Lie-group $\Pin_4$ is isomorphic to the semidirect product $(\SU_2\times \SU_2)\timesv \Z/2$ where $\Z/2$ operates by flipping the factors. Using this structure theorem we prove a classification theorem for $\Pin_4$-bundles over a finite $4$-complex $X$.
 MSC Classifications: 55N25 - Homology with local coefficients, equivariant cohomology 55R10 - Fiber bundles 57S15 - Compact Lie groups of differentiable transformations