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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, 55R10, 57S15 show english descriptions Homology with local coefficients, equivariant cohomology
Fiber bundles
Compact Lie groups of differentiable transformations
55N25 - Homology with local coefficients, equivariant cohomology
55R10 - Fiber bundles
57S15 - Compact Lie groups of differentiable transformations
 

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