On the space of maps inducing isomorphic connections

Ramadas, T. R.

doi:10.5802/aif.868

Ramadas, T. R.

Annales de l'Institut Fourier, Volume 32 (1982) no. 1, pp. 263-276

Abstract (Original language)
Résumé

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.

Soit $ω$ la connexion universelle du fibré $E U (n) \to B U (n)$ . Étant donné un $U (n)$ -fibré principal $P \to M$ muni d’une connexion $A$ , on détermine le type homotopique de l’espace des applications de $M$ dans $B U (n)$ telles que $(φ^{+} E U (n), φ^{+} ω)$ soit isomorphe à $(P, A)$ . (On désigne par $φ^{+}$ l’image réciproque.)

MR Zbl

DOI: 10.5802/aif.868

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     author = {Ramadas, T. R.},
     title = {On the space of maps inducing isomorphic connections},
     journal = {Annales de l'Institut Fourier},
     pages = {263--276},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {1},
     year = {1982},
     doi = {10.5802/aif.868},
     mrnumber = {84h:53038},
     zbl = {0466.55011},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.868/}
}

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Ramadas, T. R. On the space of maps inducing isomorphic connections. Annales de l'Institut Fourier, Volume 32 (1982) no. 1, pp. 263-276. doi: 10.5802/aif.868

References
Cited by

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[4] M.S. Narasimhan and S. Ramanan, Existence of universal connections, Amer. J. Math., 83 (1961), 573-572. | Zbl | MR

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[7] I.M. Singer, Some remarks on the Gribov ambiguity, Commun. Math. Phys., 60 (1978), 7-12. | Zbl | MR

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