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Анотація
В представленому огляді наведено кілька версій когомологій Флоєра"=Новікова а також встановлено кілька нових фактів. Зокрема, отримано нижню межу для числа симплектичних нерухомих точок невиродженого симплектоморфізма, який є симплектоморфно ізотопний до тотожного відображення тотожності, на компактному симплектичному многовиді. Ця межа є точнішою ніж отримана раніше в роботах [14,10]
Ключові слова:
симплектичні нерухомі точки, гомології Флоєра-Новікова
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Як цитувати
Ono, K., & Le, H. (2020). Когомології Флоєра-Новікова та симплектичні нерухомі точки,. Proceedings of the International Geometry Center, 13(4), 89-115. https://doi.org/10.15673/tmgc.v13i4.1809
Розділ
Статті
Посилання
1. Michael Farber. Topology of closed one-forms, volume 108 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2004, doi: http://dx.doi.org/10.1090/surv/108.
2. Andreas Floer. Morse theory for Lagrangian intersections. J. Differential Geom., 28(3):513-547, 1988, http://projecteuclid.org/euclid.jdg/1214442477.
3. Andreas Floer. Symplectic fixed points and holomorphic spheres. Comm. Math. Phys., 120(4):575-611, 1989, http://projecteuclid.org/euclid.cmp/1104177909.
4. Kenji Fukaya, Kaoru Ono. Arnold conjecture and Gromov-Witten invariant. Topology, 38(5):933-1048, 1999, doi: http://dx.doi.org/10.1016/S0040-9383(98)00042-1.
5. Kenji Fukaya, Kaoru Ono. Floer homology and Gromov-Witten invariant over integer of general symplectic manifolds-summary. In Taniguchi Conference on Mathematics Nara '98, volume 31 of Adv. Stud. Pure Math., pages 75-91. Math. Soc. Japan, Tokyo, 2001, doi: http://dx.doi.org/10.2969/aspm/03110075.
6. H. Hofer, D. A. Salamon. Floer homology and Novikov rings. In The Floer memorial volume, volume 133 of Progr. Math., pages 483-524. Birkhauser, Basel, 1995.
7. Gang Liu, Gang Tian. Floer homology and Arnold conjecture. J. Differential Geom., 49(1):1-74, 1998, http://projecteuclid.org/euclid.jdg/1214460936.
8. K. Ono. Floer-Novikov cohomology and the flux conjecture. Geom. Funct. Anal., 16(5):981-1020, 2006, doi: http://dx.doi.org/10.1007/s00039-006-0575-6.
9. Kaoru Ono. On the Arnolcprime d conjecture for weakly monotone symplectic manifolds. Invent. Math., 119(3):519-537, 1995, doi: http://dx.doi.org/10.1007/BF01245191.
10. Kaoru Ono. Floer-Novikov cohomology and symplectic fixed points. volume 3, pages 545-563. 2005, http://projecteuclid.org/euclid.jsg/1154467629. Conference on Symplectic Topology.
11. Kaoru Ono, Andrei Pajitnov. On the fixed points of a Hamiltonian diffeomorphism in presence of fundamental group. In Essays in mathematics and its applications, pages 199-228. Springer, [Cham], 2016.
12. Andrei V. Pajitnov. Circle-valued Morse theory, volume 32 of De Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 2006, doi: http://dx.doi.org/10.1515/9783110197976.
13. L^e H^ong V^an. The Calabi invariant and the least number of periodic solutions of locally Hamiltonian equations. arXiv:1511.00638.
14. L^e H^ong V^an, Kaoru Ono. Symplectic fixed points, the Calabi invariant and Novikov homology. Topology, 34(1):155-176, 1995, doi: http://dx.doi.org/10.1016/0040-9383(94)E0015-C
2. Andreas Floer. Morse theory for Lagrangian intersections. J. Differential Geom., 28(3):513-547, 1988, http://projecteuclid.org/euclid.jdg/1214442477.
3. Andreas Floer. Symplectic fixed points and holomorphic spheres. Comm. Math. Phys., 120(4):575-611, 1989, http://projecteuclid.org/euclid.cmp/1104177909.
4. Kenji Fukaya, Kaoru Ono. Arnold conjecture and Gromov-Witten invariant. Topology, 38(5):933-1048, 1999, doi: http://dx.doi.org/10.1016/S0040-9383(98)00042-1.
5. Kenji Fukaya, Kaoru Ono. Floer homology and Gromov-Witten invariant over integer of general symplectic manifolds-summary. In Taniguchi Conference on Mathematics Nara '98, volume 31 of Adv. Stud. Pure Math., pages 75-91. Math. Soc. Japan, Tokyo, 2001, doi: http://dx.doi.org/10.2969/aspm/03110075.
6. H. Hofer, D. A. Salamon. Floer homology and Novikov rings. In The Floer memorial volume, volume 133 of Progr. Math., pages 483-524. Birkhauser, Basel, 1995.
7. Gang Liu, Gang Tian. Floer homology and Arnold conjecture. J. Differential Geom., 49(1):1-74, 1998, http://projecteuclid.org/euclid.jdg/1214460936.
8. K. Ono. Floer-Novikov cohomology and the flux conjecture. Geom. Funct. Anal., 16(5):981-1020, 2006, doi: http://dx.doi.org/10.1007/s00039-006-0575-6.
9. Kaoru Ono. On the Arnolcprime d conjecture for weakly monotone symplectic manifolds. Invent. Math., 119(3):519-537, 1995, doi: http://dx.doi.org/10.1007/BF01245191.
10. Kaoru Ono. Floer-Novikov cohomology and symplectic fixed points. volume 3, pages 545-563. 2005, http://projecteuclid.org/euclid.jsg/1154467629. Conference on Symplectic Topology.
11. Kaoru Ono, Andrei Pajitnov. On the fixed points of a Hamiltonian diffeomorphism in presence of fundamental group. In Essays in mathematics and its applications, pages 199-228. Springer, [Cham], 2016.
12. Andrei V. Pajitnov. Circle-valued Morse theory, volume 32 of De Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 2006, doi: http://dx.doi.org/10.1515/9783110197976.
13. L^e H^ong V^an. The Calabi invariant and the least number of periodic solutions of locally Hamiltonian equations. arXiv:1511.00638.
14. L^e H^ong V^an, Kaoru Ono. Symplectic fixed points, the Calabi invariant and Novikov homology. Topology, 34(1):155-176, 1995, doi: http://dx.doi.org/10.1016/0040-9383(94)E0015-C