Commuting involutions whose fixed point set consists of two special components

Pedro 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 -