Bordism-Finiteness and Semi-simple Group Actions


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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Dessai, A. Bordism-Finiteness and Semi-simple Group Actions. Geometriae Dedicata 90, 49–62 (2002).

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  • transformation groups
  • bordism groups
  • equivariant index theory
  • homotopy complex projective spaces
  • finiteness theorems