The laitinen conjecture for finite solvable oliver groups

Krzysztof Pawalowski, Toshio Sumi

Research output: Contribution to journalArticle

5 Citations (Scopus)

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(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.

Original languageEnglish
Pages (from-to)2147-2156
Number of pages10
JournalProceedings of the American Mathematical Society
Volume137
Issue number6
DOIs
Publication statusPublished - Jun 1 2009

Fingerprint

Counterexample
Fixed point
Tangent Space
Module

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 137, No. 6, 01.06.2009, p. 2147-2156.

Research output: Contribution to journalArticle

@article{17f6fe6729f94a12b91507f856eee375,
title = "The laitinen conjecture for finite solvable oliver groups",
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(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.",
author = "Krzysztof Pawalowski and Toshio Sumi",
year = "2009",
month = "6",
day = "1",
doi = "10.1090/S0002-9939-09-09719-6",
language = "English",
volume = "137",
pages = "2147--2156",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "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 -