Asian Journal of Mathematics

Volume 16 (2012)

Number 2

On the conjecture of Kosinowski

Pages: 271 – 278

DOI: http://dx.doi.org/10.4310/AJM.2012.v16.n2.a5

Authors

Hyun Woong Cho

Jin Hong Kim

Han Chul Park

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.

Keywords

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

2010 Mathematics Subject Classification

55N91, 57S25

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