One fixed point actions on spheres. I,II

DOI10.1016/0001-8708(82)90052-4zbMath0502.57021OpenAlexW1970316726MaRDI QIDQ1172847

Ted Petrie

Publication date: 1982

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(82)90052-4

zbMATH Keywords

equivariant surgeryequivariant transversalitysmooth actions of a compact Lie group on a homotopy sphere

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Surgery and handlebodies (57R65) Finite transformation groups (57S17)

Related Items

\(K\)-theoretic groups with positioning map and equivariant surgery ⋮ Induction theorems of surgery obstruction groups ⋮ Equivariant surgery theory: Construction of equivariant normal maps ⋮ Bak's work on theK-theory of rings ⋮ $\mathrm {SL}(2, 5)$ Has no Smooth Effective One-fixed-point Action on $S^8$ ⋮ Gap conditions for representations of symmetric groups ⋮ Isovariant mappings of degree 1 and the gap hypothesis ⋮ Spheres not admitting smooth odd-fixed-point actions of \(S_5\) and \(SL(2, 5)\) ⋮ Exclusions of smooth actions on spheres of the non-split extension of \(C_2\) by \(\mathrm{SL}(2,5)\) ⋮ Construction of one-fixed-point actions on spheres of nonsolvable groups. I ⋮ One fixed point actions on spheres. I,II ⋮ One fixed point actions on low-dimensional spheres ⋮ Topological invariants of real algebraic actions ⋮ Equivariant Intersection Theory and Surgery Theory for Manifolds with Middle Dimensional Singular Sets ⋮ Smith equivalence of representations ⋮ Bak groups and equivariant surgery. II ⋮ Most standard spheres have smooth one fixed point actions of \(A_ 5\). II ⋮ On one fixed point actions on spheres ⋮ Tangential representations of one-fixed-point actions on spheres and Smith equivalence ⋮ Group actions having one fixed point ⋮ Nonlinear analogs of linear group actions on spheres ⋮ Spherical isotropy representations

Cites Work

• One fixed point actions on spheres. I,II
• Surgery on products with finite fundamental group
• The index of elliptic operators. II
• A Lefschetz fixed point formula for elliptic complexes. II: Applications
• Fiberings with singularities
• 𝐺 surgery. II
• Whitehead torsion
• The existence of free metacyclic actions on homotopy spheres
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