$Z{₂}^k$-actions fixing point ∪ Vⁿ

Pedro 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 -