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ЖУРНАЛЫ // Алгебра и анализ

Алгебра и анализ, 2014, том 26, выпуск 3, страницы 131–158 (Mi aa1386)

Morse–Novikov theory, Heegaard splittings, and closed orbits of gradient flows
H. Goda, H. Matsuda, A. Pajitnov

Список литературы

1. Dold A., Lectures on algebraic topology, Grundlehren Math. Wiss., 200, Springer, Berlin, 1972  mathscinet  zmath
2. Donaldson S. K., “Topological field theories and formulae of Casson and Meng-Taubes”, Proc. of the Kirbyfest (Berkeley, CA, 1998), Geom. Topol. Monogr., 2, Geom. Topol. Publ., Coventry, 1999, 87–102  crossref  mathscinet  zmath
3. Fintushel R., Stern R., “Knots, links, and $4$-manifolds”, Invent. Math., 134:2 (1998), 363–400  crossref  mathscinet  zmath  adsnasa  isi
4. Gabai D., “Foliations and the topology of $3$-manifolds”, J. Differential Geom., 18:3 (1983), 445–503  mathscinet  zmath  isi
5. Gabai D., “Detecting fibred links in $S^3$”, Comment. Math. Helv., 61:4 (1986), 519–555  crossref  mathscinet  zmath  isi
6. Goda H., “Heegaard splitting for sutured manifolds and Murasugi sum”, Osaka J. Math., 29:1 (1992), 21–40  mathscinet  zmath  isi
7. Goda H., “On handle number of Seifert surfaces in $S^3$”, Osaka J. Math., 30:1 (1993), 63–80  mathscinet  zmath  isi
8. Goda H., “Circle valued Morse theory for knots and links”, Floer Homology, Gauge Theory, and Low-dimensional Topology, Clay Math. Proc., 5, Amer. Math. Soc., Providence, RI, 2006, 71–99  mathscinet  zmath
9. Goda H., Pajitnov A., “Twisted Novikov homology and circle-valued Morse theory for knots and links”, Osaka J. Math., 42:3 (2005), 557–572  mathscinet  zmath  isi
10. Goda H., Pajitnov A., “Dynamics of gradient flows in the half-transversal Morse theory”, Proc. Japan Acad. Ser. A Math. Sci., 85:1 (2009), 6–10  crossref  mathscinet  zmath  isi
11. Hutchings M., Lee Y-J., “Circle-valued Morse theory, Reidemeister torsion, and Seiberg–Witten invariants of $3$-manifolds”, Topology, 38:4 (1999), 861–888  crossref  mathscinet  zmath  isi
12. Hutchings M., Lee Y-J., “Circle-valued Morse theory and Reidemeister torsion”, Geom. Topol., 3 (1999), 369–396  crossref  mathscinet  zmath  isi
13. Lei F., “On stability of Heegaard splittings”, Math. Proc. Cambridge Philos. Soc., 129:1 (2000), 55–57  crossref  mathscinet  zmath
14. Mark T., “Torsion, TQFT and Seiberg–Witten invariants of $3$-manifolds”, Geom. Topol., 6 (2002), 27–58  crossref  mathscinet  zmath  isi
15. Meng G., Taubes C., “$\underline{SW}=$ Milnor torsion”, Math. Res. Lett., 3:5 (1996), 661–674  crossref  mathscinet  zmath
16. Milnor J., “Infinite cyclic coverings”, Conf. on the Topology of Manifolds (Michigan State Univ., Mich., 1967), Prindle, Weber & Schmidt, Boston, Mass., 1968, 115–133  mathscinet
17. Morita S., Geometry of characteristic classes, Iwanami Ser. Modern Math., Transl. Math. Monogr., 199, Amer. Math. Soc., Providence, RI, 2001  mathscinet  zmath
18. Новиков С. П., “Многозначные функции и функционалы. Аналог теории Морса”, Докл. АН СССР, 260:1 (1981), 31–35  mathnet  mathscinet  zmath
19. Пажитнов А. В., “Простой гомотопический тип комплекса Новикова и $\zeta$-функция Лефшеца градиентного потока”, Успехи мат. наук, 54:1 (1999), 117–170  mathnet  crossref  mathscinet  zmath; (9 July 1997), arXiv: dg-ga/9706014
20. Pajitnov A., Circle-valued Morse theory, de Gruyter Stud. Math., 32, Walter de Gruyter & Co., Berlin, 2006  crossref  mathscinet  zmath
21. Пажитнов А. В., Рудолф Л., Вебер K., “Число Морса–Новикова для узлов и зацеплений”, Алгебра и анализ, 13:3 (2001), 105–118  mathnet  mathscinet  zmath
22. Scharlemann M., “Sutured manifolds and generalized Thurston norms”, J. Differential Geom., 29:3 (1989), 557–614  mathscinet  zmath  isi
23. Scharlemann M., Thompson A., “Heegaard splittings of $(surface)\times I$ are standard”, Math. Ann., 295:3 (1993), 549–564  crossref  mathscinet  zmath  isi
24. Turaev V., “A combinatorial formulation for the Seiberg–Witten invariants of $3$-manifolds”, Math. Res. Lett., 5:5 (1998), 583–598  crossref  mathscinet  zmath  isi


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