Commuting involutions whose fixed point set consists of two special components

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

Abstrakty

EN

Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property 𝓗 when it has the following property: if $N^m$ is any smooth 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. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces $RP^{2n}$, $CP^{2n}$ and $HP^{2n}$, and the connected sum of $RP^{2n}$ and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere and n is not a power of 2. In this paper we describe the equivariant cobordism classification of smooth actions $(M^m; Φ)$ of the group $Z₂^k$ on closed smooth m-dimensional manifolds $M^m$ for which the fixed point set of the action consists of two components K and L with property 𝓗, and where dim(K) < dim(L). The description is given in terms of the set of equivariant cobordism classes of involutions fixing K ∪ L.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 201
• Numer: 3
• Strony: 241-259

Daty

wydano

2008

Twórcy

autor

Pedro L. Q. Pergher

• Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil

autor

Rogério de Oliveira

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

Identyfikatory

DOI

10.4064/fm201-3-3