Equivariant periodicity for compact group actions
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Shmuel Weinberger
Abstract
For a manifold M, the structure set S (M, rel ∂ ) is the collection of manifolds homotopy equivalent to M relative to the boundary. Siebenmann [R. C. Kirby, L. C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations. Princeton Univ. Press 1977] showed that in the topological category, the structure set is 4-periodic: S (M, rel ∂ ) ≅ S (MｘD 4, rel ∂ ) up to a copy of ℤ. The periodicity has been extended to topological manifolds with homotopically stratified group actions for various representations in place of D 4, including twice any complex representation of a compact abelian group. In this paper, we extend the result to twice any complex representation of a compact Lie group. We also prove the bundle version of the periodicity.
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Semifield flocks, eggs, and ovoids of Q (4,q)
- Index of speciality and arithmetically Gorenstein subschemes
- Polar spaces embedded in projective spaces
- Equivariant periodicity for compact group actions
- The finiteness property and Łojasiewicz inequality for global semianalytic sets
- 3-dimensional loops on non-solvable reductive spaces
- A characterization of the P-geometry for M23
- A lower bound for the second sectional geometric genus of polarized manifolds
- On the geometry of linear involutions
- Removable singularities for p-harmonic maps: the subquadratic case
- Division algebras with an anti-automorphism but with no involution
