Frontiers of Mathematics in China >
Number of fixed points for unitary Tn−1-manifold
Received date: 24 Jun 2019
Accepted date: 03 Aug 2019
Published date: 15 Aug 2019
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Let M be a 2n-dimensional closed unitary manifold with a Tn−1-action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary Tn−1-manifold M is just determined by the equivariant Chern numbers [M],where ω= (i1, i2, ..., i6) are the multi-indexes for all i1, i2, ..., i6∈. Then we show that if Mdoes not bound equivariantly, then the number of fixed points is greater than or equal to , where denotes the minimum integer no less than n/6.
Shiyun WEN , Jun MA . Number of fixed points for unitary Tn−1-manifold[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 819 -831 . DOI: 10.1007/s11464-019-0785-5
1 |
Borel A, Hirzebruch F. Characteristic classes and homogeneous spaces, I. Amer J Math, 1958, 80(2): 458–538
|
2 |
Borel A, Hirzebruch F. Characteristic classes and homogeneous spaces, II. Amer J Math, 1959, 81(2): 315–382
|
3 |
Buchstaber V M, Krichever I M. Geometry, Topology, and Mathematical Physics. S. P. Novikov’s Seminar: 2006-2007. Amer Math Soc Transl Ser 2, Vol 224. Providence: Amer Math Soc, 2008
|
4 |
Buchstaber V M, Panov T E. Toric Topology. Math Surveys Monogr, Vol 204. Providence: Amer Math Soc, 2015
|
5 |
Cho H W, Kim J H, Park H C. On the conjecture of Kosniowski. Asian J Math, 2012, 16(2): 271–278
|
6 |
Darby A. Torus manifolds in equivariant complex bordism. Topology Appl, 2015, 189: 31–64
|
7 |
Guillemin V, Ginzburg V, Karshon Y. Moment Maps, Cobordisms, and Hamiltonian Group Actions. Math Surveys Monogr, Vol 98. Providence: Amer Math Soc, 2002
|
8 |
Hattori A. S1-actions on unitary manifolds and quasi-ample line bundles. J Fac Sci Univ Tokyo, Sect IA Math, 1985, 31: 433–486
|
9 |
Jang D. Circle actions on almost complex manifolds with 4 fixed points. Math Z, 2019, https://doi.org/10.1007/s00209-019-02267-z
|
10 |
Jang D, Blackburn N. Circle actions on almost complex manifolds with isolated fixed points. J Geom Phys, 2017, 119: 187–192
|
11 |
Kosniowski C. Some formulae and conjectures associated with circle actions. In: Koschorke U, Neumann W D, eds. Topology Symposium Siegen 1979: Proceedings of a Symposium Held at the University of Siegen, June 14–19, 1979. Lecture Notes in Math, Vol 788. Berlin: Springer, 1980, 331–339
|
12 |
Kustarev A A. Almost complex circle actions with few fixed points. Russian Math Surveys, 2013, 68(3): 574–576
|
13 |
Li P, Liu K. Some remarks on circle action on manifolds. Math Res Lett, 2011, 18(3): 437–446
|
14 |
Lü Z, Tan Q. Equivariant Chern numbers and the number of fixed points for unitary torus manifolds. Math Res Lett, 2011, 18(6): 1319–1325
|
15 |
Lü Z, Wang W. Equivariant cohomology Chern numbers determine equivariant unitary bordism for torus groups. Algebr Geom Topol, 2018, 18: 4143–4160
|
16 |
Musin O R. Circle actions with two fixed points. Math Notes, 2016, 100: 636–638
|
17 |
Pelayo A, Tolman S. Fixed points of symplectic periodic flows. Ergodic Theory Dynam Systems, 2011, 31(4): 1237–1247
|
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