On the conjecture of Kosinowski

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.

Keywords

Unitary G-manifolds, ABBV localization theorem, isolated fixed points, Kosniowski’s conjecture

2010 Mathematics Subject Classification

55N91, 57S25

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Published 6 April 2012