• Corpus ID: 237142439

Circle actions on six dimensional oriented manifolds with isolated fixed points

@inproceedings{Jang2021CircleAO,
  title={Circle actions on six dimensional oriented manifolds with isolated fixed points},
  author={Donghoon Jang},
  year={2021}
}

• D. Jang
• Published 17 August 2021
• Mathematics

Circle actions and torus actions on compact oriented 4manifolds were studied and classified in 1970’s but completely classifying those actions on 6-manifolds is challenging and known results on 6manifolds require strong assumptions on actions and/or manifolds. In this paper, we study circle actions on compact oriented 6-manifolds with finite fixed point sets. We show that for any such manifold, we can successively take equivariant connected sums at fixed points with S, CP, and 6-dimensional analogue Z1 and Z2 of the Hirzebruch surfaces (and these with opposite orientations) to a fixed point free action on a compact oriented 6-manifold. In particular, S, CP, Z1, and Z2 are generators of cobordism classes of 6-dimensional compact oriented S-manifolds with finite fixed point sets. This also classifies the fixed point data (weights at the fixed points) of any such manifold that we can convert it to the empty set by performing a combination of a number of types of operations.