论文信息 - ON THE CONJECTURE OF KOSNIOWSKI

ON THE CONJECTURE OF KOSNIOWSKI

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-manifold with only isolated fixed points. More precisely, if certain S-equivariant Chern characteristic number of a unitary S-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-equivariant Chern number. In addition, we also deal with the case of oriented unitary Tn-manifolds.

H. Cho | Hanchul Park | Jin Hong Kim

[1] Ping Li. Cohomology obstructions to certain circle actions , 2011 .

[2] Qiangbo Tan,et al. Equivariant Chern numbers and the number of fixed points for unitary torus manifolds , 2011, 1103.6173.

[3] Kefeng Liu,et al. Some remarks on circle action on manifolds , 2010, 1008.4826.

[4] Á. Pelayo,et al. Fixed points of symplectic periodic flows , 2010, Ergodic Theory and Dynamical Systems.

[5] P. Ding. Topological obstructions to certain Lie group actions on manifolds , 2005 .

[6] M. Masuda. Unitary toric manifolds, multi-fans and equivariant index , 1999 .

[7] S. Tolman,et al. On semifree symplectic circle actions with isolated fixed points , 1998, math/9812015.

[8] C. Kosniowski. Homology spheres andS1-actions , 1983 .

[9] C. Kosniowski. Some formulae and conjectures associated with circle actions , 1980 .