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Bordism-Finiteness and Semi-simple Group Actions

Research paper by Anand Dessai

Indexed on: 01 Mar '02Published on: 01 Mar '02Published in: Geometriae Dedicata



Abstract

We give bordism-finiteness results for smooth S3-manifolds. Consider the class of oriented manifolds which admit an S1-action with isolated fixed points such that the action extends to an S3-action with fixed point. We exhibit various subclasses, characterized by an upper bound for the Euler characteristic and properties of the first Pontryagin class p1, for example p1 = 0, which contain only finitely many oriented bordism types in any given dimension. Also we show finiteness results for homotopy complex projective spaces and complete intersections with S3-action as above.