Smooth actions of finite Oliver groups on spheres

• Published in: Topology (Oxford) Vol. 42; no. 2; pp. 395 - 421
• Main Authors: Morimoto, Masaharu, Pawałowski, Krzysztof
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2003
• Subjects: Equivariant bundle extension; Equivariant bundle subtraction; Equivariant normal bundle; Equivariant surgery; Equivariant thickening; Fixed point set; Gap group; Oliver group; Oliver obstruction; Smooth action on sphere; Oliver obstruction; Equivariant thickening; Equivariant bundle extension; Fixed point set; Equivariant bundle subtraction; Oliver group; Equivariant surgery; 55R50; 57R65; 55M35; Smooth action on sphere; 55R91; 55R35; 57S25; 57S17; 57R67; Equivariant normal bundle; Gap group
• ISSN: 0040-9383; 1879-3215
• DOI: 10.1016/S0040-9383(02)00008-3

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.