Smooth actions of finite Oliver groups on spheres |
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Authors: | Masaharu Morimoto Krzysztof Pawa?owski |
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Institution: | a Department of Mathematical and Environmental Sciences, Faculty of Environmental Science and Technology, Okayama University, Tsushimanaka 3-1-1, Okayama 700-8530, Japan b Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland |
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Abstract: | In this article, we deal with the following two questions. For smooth actions of a given finite group G on spheres S, which smooth manifolds F occur as the fixed point sets in S, and which real G-vector bundles ν over F occur as the equivariant normal bundles of F in S? We focus on the case G is an Oliver group and answer both questions under some conditions imposed on G, F, and ν. We construct smooth actions of G on spheres by making use of equivariant surgery, equivariant thickening, and Oliver's equivariant bundle extension method modified by an equivariant wegde sum construction and an equivariant bundle subtraction procedure. |
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Keywords: | 57S17 57S25 55M35 55R35 55R50 55R91 57R65 57R67 |
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