### Abstract

For smooth actions of G on spheres with exactly two fixed points, the Laitinen Conjecture proposed an answer to the Smith question about the G-modules determined on the tangent spaces at the two fixed points. Morimoto obtained the first counterexample to the Laitinen Conjecture for G = Aut(A_{6}). By answering the Smith question for some finite solvable Oliver groups G,we obtain new counterexamples to the Laitinen Conjecture, presented for the first time in the case where G is solvable.

Original language | English |
---|---|

Pages (from-to) | 2147-2156 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*137*(6), 2147-2156. https://doi.org/10.1090/S0002-9939-09-09719-6

**The laitinen conjecture for finite solvable oliver groups.** / Pawalowski, Krzysztof; Sumi, Toshio.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 6, pp. 2147-2156. https://doi.org/10.1090/S0002-9939-09-09719-6

}

TY - JOUR

T1 - The laitinen conjecture for finite solvable oliver groups

AU - Pawalowski, Krzysztof

AU - Sumi, Toshio

PY - 2009/6/1

Y1 - 2009/6/1

N2 - For smooth actions of G on spheres with exactly two fixed points, the Laitinen Conjecture proposed an answer to the Smith question about the G-modules determined on the tangent spaces at the two fixed points. Morimoto obtained the first counterexample to the Laitinen Conjecture for G = Aut(A6). By answering the Smith question for some finite solvable Oliver groups G,we obtain new counterexamples to the Laitinen Conjecture, presented for the first time in the case where G is solvable.

AB - For smooth actions of G on spheres with exactly two fixed points, the Laitinen Conjecture proposed an answer to the Smith question about the G-modules determined on the tangent spaces at the two fixed points. Morimoto obtained the first counterexample to the Laitinen Conjecture for G = Aut(A6). By answering the Smith question for some finite solvable Oliver groups G,we obtain new counterexamples to the Laitinen Conjecture, presented for the first time in the case where G is solvable.

UR - http://www.scopus.com/inward/record.url?scp=77951065150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951065150&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-09-09719-6

DO - 10.1090/S0002-9939-09-09719-6

M3 - Article

VL - 137

SP - 2147

EP - 2156

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -