# Commuting involutions whose fixed point set consists of two special components

Pedro L. Q. Pergher; Rogério de Oliveira

Fundamenta Mathematicae (2008)

- Volume: 201, Issue: 3, page 241-259
- ISSN: 0016-2736

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topPedro L. Q. Pergher, and Rogério de Oliveira. "Commuting involutions whose fixed point set consists of two special components." Fundamenta Mathematicae 201.3 (2008): 241-259. <http://eudml.org/doc/282845>.

@article{PedroL2008,

abstract = {Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property 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 , and where dim(K) < dim(L). The description is given in terms of the set of equivariant cobordism classes of involutions fixing K ∪ L.},

author = {Pedro L. Q. Pergher, Rogério de Oliveira},

journal = {Fundamenta Mathematicae},

keywords = {-action; fixed data; property ; simultaneous cobordism; equivariant cobordism; characteristic number; projective bundle},

language = {eng},

number = {3},

pages = {241-259},

title = {Commuting involutions whose fixed point set consists of two special components},

url = {http://eudml.org/doc/282845},

volume = {201},

year = {2008},

}

TY - JOUR

AU - Pedro L. Q. Pergher

AU - Rogério de Oliveira

TI - Commuting involutions whose fixed point set consists of two special components

JO - Fundamenta Mathematicae

PY - 2008

VL - 201

IS - 3

SP - 241

EP - 259

AB - Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property 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 , and where dim(K) < dim(L). The description is given in terms of the set of equivariant cobordism classes of involutions fixing K ∪ L.

LA - eng

KW - -action; fixed data; property ; simultaneous cobordism; equivariant cobordism; characteristic number; projective bundle

UR - http://eudml.org/doc/282845

ER -

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