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Connections with prescribed first Pontrjagin form
Authors:Mahuya Datta
Institution:Department of Pure Mathematics, University of Calcutta, 35 P. Barua Sarani, Calcutta 700019, India
Abstract:Let $P$ be a principal $O(n)$ bundle over a $C^\infty$manifold $M$ of dimension $m$. If $n\geq 5m+4+4\binom{m+1}{4}$, then we prove that every differential 4-form representing the first Pontrjagin class of $P$ is the Pontrjagin form of some connection on $P$.
Keywords:Principal bundle  connections  first Pontrjagin form
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