On an algebraic formula and applications to group action on manifolds

Abstract

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.

7 pages, revised slightly to update a new reference and reassign the credit of the idea in this note

References in corpus (1)

• Equivariant Chern numbers and the number of fixed points for unitary torus manifolds

Cited by in corpus (4)

• New tools for classifying Hamiltonian circle actions with isolated fixed points
• Log-concavity and symplectic flows
• Combinatorial identities and Chern numbers of complex flag manifolds
• Kosniowski's conjecture and weights