Correction for the paper “ S 3 -bundles and exotic actions”

T. E. Barros

Bulletin de la Société Mathématique de France (2001)

  • Volume: 129, Issue: 4, page 543-545
  • ISSN: 0037-9484

Abstract

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In [R] explicit representatives for S 3 -principal bundles over S 7 are constructed, based on these constructions explicit free S 3 -actions on the total spaces are described, with quotients exotic 7 -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic 7 -spheres that occur as quotients of the free S 3 -actions described above.

How to cite

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Barros, T. E.. "Correction for the paper “$S^3$-bundles and exotic actions”." Bulletin de la Société Mathématique de France 129.4 (2001): 543-545. <http://eudml.org/doc/272520>.

@article{Barros2001,
abstract = {In [R] explicit representatives for $S^3$-principal bundles over $S^7$ are constructed, based on these constructions explicit free $S^3$-actions on the total spaces are described, with quotients exotic $7$-spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic $7$-spheres that occur as quotients of the free $S^3$-actions described above.},
author = {Barros, T. E.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {principal bundles; exotic spheres; exotic actions},
language = {eng},
number = {4},
pages = {543-545},
publisher = {Société mathématique de France},
title = {Correction for the paper “$S^3$-bundles and exotic actions”},
url = {http://eudml.org/doc/272520},
volume = {129},
year = {2001},
}

TY - JOUR
AU - Barros, T. E.
TI - Correction for the paper “$S^3$-bundles and exotic actions”
JO - Bulletin de la Société Mathématique de France
PY - 2001
PB - Société mathématique de France
VL - 129
IS - 4
SP - 543
EP - 545
AB - In [R] explicit representatives for $S^3$-principal bundles over $S^7$ are constructed, based on these constructions explicit free $S^3$-actions on the total spaces are described, with quotients exotic $7$-spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic $7$-spheres that occur as quotients of the free $S^3$-actions described above.
LA - eng
KW - principal bundles; exotic spheres; exotic actions
UR - http://eudml.org/doc/272520
ER -

References

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  1. [1] T. Barros & A. Rigas – « The role of commutators in a non-cancellation phenomenon », Math. J. Okayama Univ. (to appear). Zbl1034.57029MR1913873
  2. [2] K. Grove & W. Ziller – « Curvature and symmetry of the Milnor spheres », Ann. of Math. (2) 152 (2000), no. 1, p. 331–367. Zbl0991.53016MR1792298
  3. [3] S. Hu – Homotopy theory, Academic Press, 1959. Zbl0088.38803MR106454
  4. [4] A. Rigas – « S 3 -bundles and exoctic actions », Bull. Soc. Math. France112 (1984), p. 69–92. Zbl0573.57010MR771919

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