Topological classification of simple Morse Bott functions on surfaces

被引：23
|
作者：
Martinez-Alfaro, J. [1 ]
Meza-Sarmiento, I. S. [2 ]
Oliveira, R. [2 ]
机构：
[1] Univ Valencia, Dept Matemat Aplicada, Burjassot, Spain
[2] Univ Sao Paulo, ICMC, Dept Matemat, Caixa Postal 668, BR-13566590 Sao Carlos, SP, Brazil
来源：
REAL AND COMPLEX SINGULARITIES | 2016年 / 675卷
关键词：
Topological invariant; Morse Bott functions; Reeb graph;
D O I：
10.1090/conm/675/13590
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a global topological classification of Morse Bott functions on orientable closed surfaces. The invariant is based on the Reeb graph of the function and the topological type of the singular level sets. Connection with other known invariants it is shown. We also prove a realization Theorem of. the Morse Bott functions.
引用
收藏
页码：165 / 179
页数：15
相关论文
共 50 条
  • [41] TOPOLOGICAL CLASSIFICATION OF GENERIC REAL MEROMORPHIC FUNCTIONS FROM COMPACT SURFACES
    Costa, Antonio F.
    Natanzon, Sergey
    Shapiro, Boris
    [J]. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2018, 43 (01) : 349 - 363
  • [42] The Morse–Bott–Kirwan condition is local
    Tara Holm
    Yael Karshon
    [J]. Research in the Mathematical Sciences, 3
  • [43] Morse–Bott split symplectic homology
    Luís Diogo
    Samuel T. Lisi
    [J]. Journal of Fixed Point Theory and Applications, 2019, 21
  • [44] A proof of the Morse-Bott lemma
    Banyaga, A
    Hurtubise, DE
    [J]. EXPOSITIONES MATHEMATICAE, 2004, 22 (04) : 365 - 373
  • [45] On the Morse–Bott property of analytic functions on Banach spaces with Łojasiewicz exponent one half
    Paul M. N. Feehan
    [J]. Calculus of Variations and Partial Differential Equations, 2020, 59
  • [46] Cobordism group of morse functions on unoriented surfaces
    Kalmár, B
    [J]. KYUSHU JOURNAL OF MATHEMATICS, 2005, 59 (02) : 351 - 363
  • [47] Symmetries groups of nice Morse functions on surfaces
    E. A. Kudryavtseva
    A. T. Fomenko
    [J]. Doklady Mathematics, 2012, 86 : 691 - 693
  • [48] Cobordism group of Morse functions on surfaces with boundary
    Saeki, Osamu
    Yamamoto, Takahiro
    [J]. REAL AND COMPLEX SINGULARITIES, 2016, 675 : 279 - 297
  • [49] On the homotopy type of spaces of Morse functions on surfaces
    Kudryavtseva, E. A.
    [J]. SBORNIK MATHEMATICS, 2013, 204 (01) : 75 - 113
  • [50] Symmetries groups of nice Morse functions on surfaces
    Kudryavtseva, E. A.
    Fomenko, A. T.
    [J]. DOKLADY MATHEMATICS, 2012, 86 (02) : 691 - 693
12345