Abstract
The aim of this paper is to address some results closely related to the conjecture
of Kosniowski about the number of xed points on a unitary S1-manifold with only
isolated xed points. More precisely, if certain S1-equivariant Chern characteristic
number of a unitary S1-manifold M is non-zero, we give a sharp lower bound on
the number of isolated xed points in terms of certain integer powers in the S1-
equivariant Chern number. In addition, in this paper we also deal with the case of
oriented unitary Tn-manifolds.