# The Equivariant Bundle Subtraction Theorem and its applications

Masaharu Morimoto; Krzysztof Pawałowski

Fundamenta Mathematicae (1999)

- Volume: 161, Issue: 3, page 279-303
- ISSN: 0016-2736

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topMorimoto, Masaharu, and Pawałowski, Krzysztof. "The Equivariant Bundle Subtraction Theorem and its applications." Fundamenta Mathematicae 161.3 (1999): 279-303. <http://eudml.org/doc/212407>.

@article{Morimoto1999,

abstract = {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.},

author = {Morimoto, Masaharu, Pawałowski, Krzysztof},

journal = {Fundamenta Mathematicae},

keywords = {equivariant bundle subtraction; smooth action on disk; fixed point set; equivariant normal bundle; the family of large subgroups of a finite group; large subgroups of a finite group},

language = {eng},

number = {3},

pages = {279-303},

title = {The Equivariant Bundle Subtraction Theorem and its applications},

url = {http://eudml.org/doc/212407},

volume = {161},

year = {1999},

}

TY - JOUR

AU - Morimoto, Masaharu

AU - Pawałowski, Krzysztof

TI - The Equivariant Bundle Subtraction Theorem and its applications

JO - Fundamenta Mathematicae

PY - 1999

VL - 161

IS - 3

SP - 279

EP - 303

AB - 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.

LA - eng

KW - equivariant bundle subtraction; smooth action on disk; fixed point set; equivariant normal bundle; the family of large subgroups of a finite group; large subgroups of a finite group

UR - http://eudml.org/doc/212407

ER -

## References

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