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On the space of maps inducing isomorphic connections

T. R. Ramadas — 1982

Annales de l'institut Fourier

Let $ω$ be the universal connection on the bundle $E U (n) \to B U (n)$ . Given a principal $U (n)$ -bundle $P \to M$ with connection $A$ , we determine the homotopy type of the space of maps $ϕ$ of $M$ into $B U (n)$ such that $(ϕ^{+} E U (n), ϕ^{+} ω)$ is isomorphic to $(P, A)$ . Here $ϕ^{+}$ denotes pull-back.

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