Deleting-Inserting Theorem for smooth actions of finite nonsolvable groups on spheres |
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Authors: | Erkki Laitinen Masaharu Morimoto Krzysztof Pawa?owski |
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Institution: | 1. Department of Mathematics, University of Helsinki, (Hallituskatu 15), P.O. Box 4, SF-00014, Finland 2. Department of Mathematics College of Liberal Arts & Sci., Okayama University, Tsushimanaka 2-1, 700, Okayama, Japan 3. Faculty of Mathematics and Informatics, University of Poznań (UAM), ul. Jana Matejki 48/49, PL-60-769, Poznań, Poland
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Abstract: | The paper presents a method which allows to construct smooth finite nonsolvable group actions on spheres with prescribed fixed
point data. The idea is to consider an action on a disk with the required fixed point data, and then to apply equivariant
surgery to the equivariant double of the disk to remove the second copy of the fixed point data. In this paper, the method
is applied to construct smooth group actions on spheres with exactly one fixed point, and more general actions with fixed
point set diffeomorphic to any given closed stably parallelizable smooth manifold. The method is expected to be useful for
constructions of smooth group actions on spheres with more complicated fixed point data.
1991Mathematics Subject Classification: 57S17, 57S25, 57R67, 57R85. |
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Keywords: | |
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