# $Z{\u2082}^{k}$-actions fixing point ∪ Vⁿ

Fundamenta Mathematicae (2002)

- Volume: 172, Issue: 1, page 83-97
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topPedro L. Q. Pergher. "$Z₂^k$-actions fixing point ∪ Vⁿ." Fundamenta Mathematicae 172.1 (2002): 83-97. <http://eudml.org/doc/282704>.

@article{PedroL2002,

abstract = {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 the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally, the result yields some new applications, namely with Vⁿ an arbitrary product of spheres and with Vⁿ any n-dimensional closed manifold with n odd.},

author = {Pedro L. Q. Pergher},

journal = {Fundamenta Mathematicae},

keywords = {-action; equivariant cobordism class; fixed point data; characteristic number; representation},

language = {eng},

number = {1},

pages = {83-97},

title = {$Z₂^k$-actions fixing point ∪ Vⁿ},

url = {http://eudml.org/doc/282704},

volume = {172},

year = {2002},

}

TY - JOUR

AU - Pedro L. Q. Pergher

TI - $Z₂^k$-actions fixing point ∪ Vⁿ

JO - Fundamenta Mathematicae

PY - 2002

VL - 172

IS - 1

SP - 83

EP - 97

AB - 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 the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally, the result yields some new applications, namely with Vⁿ an arbitrary product of spheres and with Vⁿ any n-dimensional closed manifold with n odd.

LA - eng

KW - -action; equivariant cobordism class; fixed point data; characteristic number; representation

UR - http://eudml.org/doc/282704

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.