We describe the equivariant cobordism classification of smooth actions of the group on closed smooth m-dimensional manifolds 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-6,
author = {Pedro L. Q. Pergher},
title = {$Z2^k$-actions fixing point [?] Vn},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {83-97},
zbl = {0996.57017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-6}
}
Pedro L. Q. Pergher. $Z₂^k$-actions fixing point ∪ Vⁿ. Fundamenta Mathematicae, Tome 173 (2002) pp. 83-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-6/