# Correction for the paper “${S}^{3}$-bundles and exotic actions”

Bulletin de la Société Mathématique de France (2001)

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

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topBarros, 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

top- [1] T. Barros & A. Rigas – « The role of commutators in a non-cancellation phenomenon », Math. J. Okayama Univ. (to appear). Zbl1034.57029MR1913873
- [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] S. Hu – Homotopy theory, Academic Press, 1959. Zbl0088.38803MR106454
- [4] A. Rigas – « ${S}^{3}$-bundles and exoctic actions », Bull. Soc. Math. France112 (1984), p. 69–92. Zbl0573.57010MR771919

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