Floer Homology for the Gelfand-Cetlin System

  • Yuichi Nohara
  • Kazushi Ueda
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


The Gelfand-Cetlin system is a completely integrable system on a flag manifold of type A. In contrast to the case of toric moment maps, the Gelfand-Cetlin system has non-torus Lagrangian fibers on some boundary strata of the momentum polytope. In this paper we discuss Lagrangian intersection Floer theory for torus and non-torus Lagrangian fibers of the Gelfand-Cetlin system on the three-dimensional full flag manifold and the Grassmannian of two-planes in a four-dimensional vector space.


Maslov Index Toric Manifold Floer Homology Flag Manifold Lagrangian Torus 
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Y. N. is supported by Grant-in-Aid for Young Scientists (No. 23740055). K. U. is supported by Grant-in-Aid for Young Scientists (No. 24740043).


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Faculty of EducationKagawa UniversityKagawaJapan
  2. 2.Department of Mathematics Graduate School of ScienceOsaka UniversityOsakaJapan

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