Circle actions on six dimensional oriented manifolds with isolated fixed points

Abstract

To classify a group action on a manifold, the data associated with the fixed point set is essential. In this paper, we classify the fixed point data of a circle action on a 6-dimensional compact connected oriented manifold with isolated fixed points, where the fixed point data consists of the collection of signs and weights at the fixed points. We show that this fixed point data can be reduced to the empty collection by performing a sequence of operations. Specifically, we prove that one can successively take equivariant connected sums at fixed points with $S^6$, ${\mathbb{CP}}^3$, or 6-dimensional analogues of the Hirzebruch surfaces (and their oppositely oriented counterparts), resulting in a fixed-point-free action on a compact connected oriented 6-manifold.

The previous version assumed that the isotropy submanifolds are orientable, but the new version proves the main result without this assumption

References in corpus (6)

• Circle actions on almost complex manifolds with 4 fixed points
• An Orlik-Raymond type classification of simply connected six-dimensional torus manifolds with vanishing odd degree cohomology
• Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4
• Circle actions on four dimensional almost complex manifolds with discrete fixed point sets
• Circle actions on oriented 4-manifolds
• Rigidity of elliptic genera for non-spin manifolds