On the conjecture of Kosniowski (Q436037)

Let \(M\) be a connected oriented closed unitary \(S^1\)-manifold of dimension \(2n\) having only isolated fixed points. Assume \(M\) does not bound a unitary \(S^1\)-manifold equivariantly. \textit{C. Kosniowski} has conjectured in [Topology, Proc. Symp., Siegen 1979, Lect. Notes Math. 788, 331--339 (1980; Zbl 0433.57016)] that the number of isolated fixed points of \(M\) must be greater than or equal to a linear function \(f(n)\) of \(n\).NEWLINENEWLINEThis paper addresses some results closely related to Kosniowski's conjecture: Assume \(M\) is a unitary \(S^1\)-manifold with only isolated fixed points, and assume a certain \(S^1\)-equivariant Chern characteristic number of \(M\) is non-zero. The authors give a lower bound for the number of isolated fixed points in terms of certain integer powers in the \(S^1\)-equivariant Chern number. In addition, they also consider the case of oriented unitary \(T^n\)-manifolds.