On the space of maps inducing isomorphic connections

T. R. Ramadas

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 1, page 263-276
  • ISSN: 0373-0956

Abstract

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Let ω be the universal connection on the bundle E U ( n ) B U ( n ) . Given a principal U ( n ) -bundle P 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.

How to cite

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Ramadas, T. R.. "On the space of maps inducing isomorphic connections." Annales de l'institut Fourier 32.1 (1982): 263-276. <http://eudml.org/doc/74528>.

@article{Ramadas1982,
abstract = {Let $\omega $ be the universal connection on the bundle $EU(n) \rightarrow BU(n)$. Given a principal $U(n)$-bundle $P\rightarrow M$ with connection $A$, we determine the homotopy type of the space of maps $\phi $ of $M$ into $BU(n)$ such that $(\phi ^+EU(n),\phi ^+\omega )$ is isomorphic to $(P,A)$. Here $\phi ^+$ denotes pull-back.},
author = {Ramadas, T. R.},
journal = {Annales de l'institut Fourier},
keywords = {space of maps inducing isomorphic connections; pull back of the universal connection on the universal U(n) bundle},
language = {eng},
number = {1},
pages = {263-276},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the space of maps inducing isomorphic connections},
url = {http://eudml.org/doc/74528},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Ramadas, T. R.
TI - On the space of maps inducing isomorphic connections
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 1
SP - 263
EP - 276
AB - Let $\omega $ be the universal connection on the bundle $EU(n) \rightarrow BU(n)$. Given a principal $U(n)$-bundle $P\rightarrow M$ with connection $A$, we determine the homotopy type of the space of maps $\phi $ of $M$ into $BU(n)$ such that $(\phi ^+EU(n),\phi ^+\omega )$ is isomorphic to $(P,A)$. Here $\phi ^+$ denotes pull-back.
LA - eng
KW - space of maps inducing isomorphic connections; pull back of the universal connection on the universal U(n) bundle
UR - http://eudml.org/doc/74528
ER -

References

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  1. [1] M. DUBOIS-VIOLETTE and Y. GEORGELIN, Gauge Theory in terms of projector valued fields, Physics Letters, 82B, 251 (1979). 
  2. [2] A. DOUADY, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, séminaire, Collège de France (1964-1965). 
  3. [3] V.N. GRIBOV, Quantization of nonabelian gauge theories, Nuclear Physics, B 139 (1978), 1. 
  4. [4] M.S. NARASIMHAN and S. RAMANAN, Existence of universal connections, Amer. J. Math., 83 (1961), 573-572. Zbl0114.38203MR24 #A3597
  5. [5] M.S. NARASIMHAN and T.R. RAMADAS, Geometry of SU(2) gauge-fields, Commun. Math. Phys., 67 (1979), 121-136. Zbl0418.53029MR84k:58050
  6. [6] R. SCHLAFLY, Universal Connections, Inventiones Math., 59 (1980), 59-65. Zbl0431.53028MR81f:53022
  7. [7] I.M. SINGER, Some remarks on the Gribov ambiguity, Commun. Math. Phys., 60 (1978), 7-12. Zbl0379.53009MR80d:53025

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