$Z₂^{k}$-actions with a special fixed point set

Pedro L. Q. Pergher ; Rogério de Oliveira

Fundamenta Mathematicae, Tome 185 (2005), p. 97-109 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if $N^{m}$ is any smooth and closed m-dimensional manifold with m > n and $T:N^{m} → N^{m}$ is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions $(M^{m};Φ)$ of the group $G = Z₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F. L. Capobianco, who obtained this classification for $Fⁿ = ℝP^{2r}$ (P. E. Conner and E. E. Floyd had previously shown that $ℝP^{2r}$ has the property in question). In addition, we establish some properties concerning these Fⁿ and give some new examples of these special manifolds.

Détail

Publié le : 2005-01-01

Zbl 1083.57044

EUDML-ID : urn:eudml:doc:283374