# $Z{\u2082}^{k}$-actions with a special fixed point set

Pedro L. Q. Pergher; Rogério de Oliveira

Fundamenta Mathematicae (2005)

- Volume: 186, Issue: 2, page 97-109
- ISSN: 0016-2736

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topPedro L. Q. Pergher, and Rogério de Oliveira. "$Z₂^{k}$-actions with a special fixed point set." Fundamenta Mathematicae 186.2 (2005): 97-109. <http://eudml.org/doc/283374>.

@article{PedroL2005,

abstract = {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.},

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

journal = {Fundamenta Mathematicae},

keywords = {; fixed data; characteristic number, Wu class; property ; Stiefel-Whitney},

language = {eng},

number = {2},

pages = {97-109},

title = {$Z₂^\{k\}$-actions with a special fixed point set},

url = {http://eudml.org/doc/283374},

volume = {186},

year = {2005},

}

TY - JOUR

AU - Pedro L. Q. Pergher

AU - Rogério de Oliveira

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

JO - Fundamenta Mathematicae

PY - 2005

VL - 186

IS - 2

SP - 97

EP - 109

AB - 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.

LA - eng

KW - ; fixed data; characteristic number, Wu class; property ; Stiefel-Whitney

UR - http://eudml.org/doc/283374

ER -

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