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# Asian Journal of Mathematics

## Volume 17 (2013)

### Number 2

### On an algebraic formula and applications to group action on manifolds

Pages: 383 – 390

DOI: https://dx.doi.org/10.4310/AJM.2013.v17.n2.a5

#### Authors

#### Abstract

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.

#### Keywords

group actions, fixed points, localization formulae

#### 2010 Mathematics Subject Classification

19J35, 37B05

Published 5 July 2013