Abstract
The Gauss images of isoparametric hypersurfaces in the unit standard sphere provide compact minimal (thus monotone) Lagrangian submanifolds embedded in complex hyperquadrics. Recently we used the Floer homology and the lifted Floer homology for monotone Lagrangian submanifolds in order to study their Hamiltonian non-displaceability in our recent joint paper with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka. In this note we will explain the spectral sequences for the Floer homology and the lifted Floer homology of monotone Lagrangian submanifolds and their applications to the Gauss images of isoparametric hypersurfaces. They are the main technical part in our joint work. Moreover we will suggest some related open problems for further research.
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Acknowledgements
The author sincerely would like to thank Professor Young Jin Suh (Director of RIRCM) for his leading the international joint project of submanifold theory in differential geometry and his organization of twenty times successful workshops. The author also would like to thank Dr. Hyunjin Lee for her excellent supports to those workshops. The author was partly supported by JSPS Grant-in-Aid for Scientific Research (C) No. 15K04851 and JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI”.
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Ohnita, Y. (2017). On Floer Homology of the Gauss Images of Isoparametric Hypersurfaces. In: Suh, Y., Ohnita, Y., Zhou, J., Kim, B., Lee, H. (eds) Hermitian–Grassmannian Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 203. Springer, Singapore. https://doi.org/10.1007/978-981-10-5556-0_20
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