Bordism-Finiteness and Semi-simple Group Actions |
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Authors: | Anand Dessai |
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Institution: | (1) Institut für Mathematik, Universität Augsburg, D-86159 Augsburg, Germany |
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Abstract: | We give bordism-finiteness results for smooth S
3-manifolds. Consider the class of oriented manifolds which admit an S
1-action with isolated fixed points such that the action extends to an S
3-action with fixed point. We exhibit various subclasses, characterized by an upper bound for the Euler characteristic and properties of the first Pontryagin class p
1, for example p
1 = 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 S
3-action as above. |
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Keywords: | transformation groups bordism groups equivariant index theory homotopy complex projective spaces finiteness theorems |
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