Asian Journal of Mathematics

Volume 17 (2013)

Number 2

On an algebraic formula and applications to group action on manifolds

Pages: 383 – 390



Ping Li (Department of Mathematics, Tongji University, Shanghai, China)

Kefeng Liu (Department of Mathematics, University of California at Los Angeles; Center of Mathematical Science, Zhejiang University, Hangzhou, China)


In this paper we consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound of the number of fixed points. We also give an obstruction to the existence of $\mathbb{Z}_p$ action on manifolds with isolated fixed points when $p$ is a prime.


group actions, fixed points, localization formulae

2010 Mathematics Subject Classification

19J35, 37B05

Published 5 July 2013