- Tytuł:
- The Equivariant Bundle Subtraction Theorem and its applications
- Autorzy:
-
Morimoto, Masaharu
Pawałowski, Krzysztof - Powiązania:
- https://bibliotekanauki.pl/articles/1205192.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
equivariant bundle subtraction
smooth action on disk
fixed point set
equivariant normal bundle
the family of large subgroups of a finite group - Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1999, 161, 3; 279-303
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł