Bordism-finiteness and semi-simple group actions

Details Bordism-finiteness and semi-simple group actions Bordism-finiteness and semi-simple group actions

2000-03-27

arxiv.org/abs/math/0003176v2

Geometriae Dedicata 90, (2002), pp. 49-62

Mathematics

Geometric Topology

to appear in Geometriae Dedicata, minor changes, one reference changed

Scientific paper

We give bordism-finiteness results for manifolds with semi-simple group action. Consider the class of oriented manifolds which admit a circle 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 Pontrjagin class, 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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