Simplifying group actions

The equivariant blow-up construction can simplify the orbit structure of a G-manifold. For abelian G the action can be simplified to an action in which all isotropy subgroups are Z 2-vector spaces and the codimension of the set of points having any isotropy subgroup is just the dimension of that sub...

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Bibliographic Details
Published in:Topology and its applications 1997, Vol.75 (1), p.13-31
Main Author: Wasserman, Arthur G.
Format: Article
Language:English
Subjects:
Blowup
Transformation groups
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Summary:The equivariant blow-up construction can simplify the orbit structure of a G-manifold. For abelian G the action can be simplified to an action in which all isotropy subgroups are Z 2-vector spaces and the codimension of the set of points having any isotropy subgroup is just the dimension of that subgroup as a Z 2-vector space. Such actions are called nonsingular. Nonsingular actions have smooth quotient spaces (with corners). Moreover, the tangent bundle of a nonsingular action of an abelian group G on M can be written as a direct sum of the tangent bundle of the quotient manifold plus a sum of line bundles which are the extensions (to the whole of M) of the normal bundles of the various fixed point sets.
ISSN:0166-8641
1879-3207
DOI:10.1016/S0166-8641(96)00084-3