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

• Autorzy: Pedro L. Q. Pergher , Rogério de Oliveira
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57R85: Equivariant cobordism
• 57R75: O - and SO -cobordism

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 186
• Numer: 2
• Strony: 97-109

Daty

wydano

2005

Twórcy

autor

Pedro L. Q. Pergher

• Centro de Ciências Exatas e Tecnologia, Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676; CEP 13.565-905, São Carlos, SP, Brazil

autor

Rogério de Oliveira

• Departamento de Ciências Exatas, Campus Universitário de Três Lagoas, Universidade Federal de Mato Grosso do Sul, Caixa Postal 210; CEP 79603-011, Três Lagoas, MS, Brazil

Identyfikatory

DOI

10.4064/fm186-2-1