ON THE CONJECTURE OF KOSNIOWSKI

Abstract

The aim of this paper is to address some results closely related to the conjecture of Kosniowski about the number of fixed points on a unitary S-1-manifold with only isolated fixed points. More precisely, if certain S-1-equivariant Chern characteristic number of a unitary S-1-manifold M is non-zero, we give a sharp (in certan cases) lower bound on the number of isolated fixed points in terms of certain integer powers in the S-1-equivariant Chern number. In addition, we also deal with the case of oriented unitary T-n-manifolds.