본문 바로가기
KERD
논문KCI 등재

On non-displaceable Lagrangian submanifolds in two-step flag varieties

김유식
대한수학회 (The Korean Mathematical Society)|2023.09|대한수학회지 (Journal of the KMS)|제60권 제5호|pp. 1109-1133|DOI 10.4134/JKMS.j230098

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Floer cohomologyGelfand--Zeitlin systemspartial flag manifoldsnon-displaceable Lagrangianspotential functions
주제분류수학

초록

We prove that the two-step flag variety $\mcal{F}\ell(1,n;n+1)$ carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3 \times T^{2n-4}$ and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n > 2$.

Abstract

We prove that the two-step flag variety $\mcal{F}\ell(1,n;n+1)$ carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3 \times T^{2n-4}$ and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n > 2$.

참고문헌 (24)

  1. B. H. An, "On the f-vectors of Gelfand-Cetlin polytopes", European J. Combin, 67, pp.61~77 (2018)[DOI]
  2. D. Bouloc, "Singular fibres of the Gelfand-Cetlin system on u(n)∗", Philos. Trans. Roy. Soc. A, 376(2131), pp.28~ (2018)[DOI]
  3. J. D. Carlson, "The topology of Gelfand-Zeitlin fibers", ~ (2021)
  4. C.-H. Cho, "Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus", Int. Math. Res. Not, 2004(35), pp.1803~1843 (2004)[DOI]
  5. Y. Cho, "Lagrangian fibers of Gelfand-Cetlin systems of SO(n)-type", Transform. Groups, 25(4), pp.1063~1102 (2020)[DOI]
  6. Y. Cho, "Monotone Lagrangians in flag varieties", Int. Math. Res. Not. IMRN, 2021(18), pp.13892~13945 (2021)[DOI]
  7. Y. Cho, "Lagrangian fibers of Gelfand-Cetlin systems", Adv. Math, 372, pp.107304~ (2020)[DOI]
  8. Y. Cho, "A critical point analysis of Landau-Ginzburg potentials with bulk in Gelfand-Cetlin systems", Kyoto J. Math, 61(2), pp.259~304 (2021)[DOI]
  9. C.-H. Cho, "Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds", Asian J. Math, 10(4), pp.773~814 (2006)[DOI]
  10. C.-H. Cho, "Holomorphic orbi-discs and Lagrangian Floer cohomology of symplectic toric orbifolds", J. Differential Geom, 98(1), pp.21~116 (2014)[DOI]
  11. J. D. Evans, "Generating the Fukaya categories of Hamiltonian Gmanifolds", J. Amer. Math. Soc, 32(1), pp.119~162 (2019)[DOI]
  12. A. Floer, "Morse theory for Lagrangian intersections", J. Differential Geom, 28(3), pp.513~547 (1988)[DOI]
  13. K. Fukaya, "Cyclic symmetry and adic convergence in Lagrangian Floer theory", Kyoto J. Math, 50(3), pp.521~590 (2010)[DOI]
  14. K. Fukaya, "Lagrangian Floer theory on compact toric manifolds I", Duke Math. J, 151(1), pp.23~174 (2010)[DOI]
  15. K. Fukaya, "Lagrangian Floer theory on compact toric manifolds II : bulk deformations", Selecta Math. (N. S.), 17(3), pp.609~711 (2011)[DOI]
  16. V. Guillemin, "The Gelfand-Cetlin system and quantization of the complex flag manifolds", J. Funct. Anal, 52(1), pp.106~128 (1983)[DOI]
  17. Y. Kim, "Detecting non-displaceable toric fibers on compact toric manifolds via tropicalizations", Internat. J. Math, 30(1, 1950003), pp.40~ (2019)[DOI]
  18. M. Kogan, "Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes", Adv. Math, 193(1), pp.1~17 (2005)[DOI]
  19. D. McDuff, "Displacing Lagrangian toric fibers via probes, in Low-dimensional and symplectic topology", Proc. Sympos. Pure Math, 82, pp.131~160 (2011), Amer. Math. Soc
  20. T. Nishinou, "Toric degenerations of Gelfand-Cetlin systems and potential functions", Adv. Math, 224(2), pp.648~706 (2010)[DOI]
  21. Y. Nohara, "Floer cohomologies of non-torus fibers of the Gelfand-Cetlin system", J. Symplectic Geom, 14(4), pp.1251~1293 (2016)[DOI]
  22. M. Pabiniak, "Displacing(Lagrangian)submanifolds in the manifolds of full flags", Adv. Geom, 15(1), pp.101~108 (2015)[DOI]
  23. C. T. Woodward, "Gauged Floer theory of toric moment fibers", Geom. Funct. Anal, 21(3), pp.680~749 (2011)[DOI]
  24. A. Zinger, "Pseudocycles and integral homology", Trans. Amer. Math. Soc, 360(5), pp.2741~2765 (2008)[DOI]

관련 논문AI추천

On toric Hamiltonian $T$-spaces with anti-symplectic involutions김진홍대한수학회 · 대한수학회보2022 · 제59권 제3호SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES김종수한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제4호Deformation rigidity of odd Lagrangian Grassmannians박경동대한수학회 · 대한수학회지2016 · 제53권 제3호On the Lagrangian fillability of almost positive linksKeiji Tagami대한수학회 · 대한수학회지2019 · 제56권 제3호Symplectic decomposition of symplectic subspaces이재혁한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제1호LENS SPACES ADMITTING MINIMAL SYMPLECTIC FILLINGS WITH THE SECOND BETTI NUMBER ONE박희상, 신동수대한수학회 · 대한수학회보2023 · 제60권 제1호

이 간행물의 다른 논문 (10건)

Almost universal sums of triangular numbers with one exception주장원pp. 931-957Forbidden theta graph, bounded spectral radius and size of non-bipartite graphsWanting Sun, Shuchao Li, Wei Weipp. 959-986Continuum-wise expansiveness for $C^1$ generic vector fields이만섭pp. 987-998The first positive and negative Dirac eigenvalues on Sasakian manifolds김의철pp. 999-1021Li-Yau gradient estimates on closed manifolds under Bakry-\'Emery Ricci curvature conditionsXingYu Song, Ling Wupp. 1023-1041
원문 보기