Circle Actions on Oriented Manifolds with Few Fixed Points
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Let the circle act on a compact oriented manifold with a dis- crete fixed point set. At each fixed point, there are positive integers called weights, which describe the local action of S1 near the fixed point. In this paper, we provide the author’s original proof that only uses the Atiyah- Singer index formula for the classification of the weights at the fixed points if the dimension of the manifold is 4 and there are at most 4 fixed points, which made the author possible to give a classification for any finite num- ber of fixed points.
Abstract
Let the circle act on a compact oriented manifold with a dis- crete fixed point set. At each fixed point, there are positive integers called weights, which describe the local action of S1 near the fixed point. In this paper, we provide the author’s original proof that only uses the Atiyah- Singer index formula for the classification of the weights at the fixed points if the dimension of the manifold is 4 and there are at most 4 fixed points, which made the author possible to give a classification for any finite num- ber of fixed points.
참고문헌 (11)
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