In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively, as the G-fixed point sets and their equivariant normal bundles for smooth G-actions on disks. In Theorems 0.2 and 0.3, we prove the corresponding results for smooth G-actions on disks with prescribed isotropy subgroups around M. In Theorems 0.4 and 0.5, for large classes of finite groups G, we explicitly describe manifolds M that occur as the G-fixed point sets for such actions on disks. These actions are expected to be useful for answering the question of which manifolds occur as the G-fixed points sets for smooth G-actions on spheres.
@article{bwmeta1.element.bwnjournal-article-fmv161i3p279bwm,
author = {Masaharu Morimoto and Krzysztof Pawa\l owski},
title = {The Equivariant Bundle Subtraction Theorem and its applications},
journal = {Fundamenta Mathematicae},
volume = {159},
year = {1999},
pages = {279-303},
zbl = {0947.57035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p279bwm}
}
Morimoto, Masaharu; Pawałowski, Krzysztof. The Equivariant Bundle Subtraction Theorem and its applications. Fundamenta Mathematicae, Tome 159 (1999) pp. 279-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p279bwm/
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