Hamiltonian non-displaceability of the Gauss images of isoprametric hypersurfaces (A survey)

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This is a survey of the joint work [13] (Bull Lond Math Soc 48(5), 802–812, 2016) with Hiroshi Iriyeh (Ibaraki U.), Hui Ma (Tsinghua U.) and Yoshihiro Ohnita (Osaka City U.). The Floer homology of Lagrangian intersections is computed in few cases. Here, we take the image L=G(N) of the Gauss map of isoparametric hypersurfaces N in Sn+1, that are minimal Lagrangian submanifolds of the complex hyperquadric Qn(ℂ). We call L Hamiltonian non-displaceable if L∩ φ (L)≠ ∅ holds for any Hamiltonian deformation φ. Hamiltonian non-displaceability is needed to define the Floer homology HF(L), since HF(L) is generated by points in L∩ φ (L). We prove the Hamiltonian non-displaceability of L=G(N) for any isoparametric hypersurfaces N with principal curvatures having plural multiplicities. The main result is stated in Sect. 4.

Original languageEnglish
Title of host publicationHermitian-Grassmannian Submanifolds
EditorsYoshihiro Ohnita, Jiazu Zhou, Byung Hak Kim, Hyunjin Lee, Young Jin Suh
PublisherSpringer New York LLC
Pages83-99
Number of pages17
ISBN (Print)9789811055553
DOIs
Publication statusPublished - 2017 Jan 1
Event20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, IWHSSS 2016 - Daegu, Korea, Republic of
Duration: 2016 Jul 262016 Jul 30

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume203
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, IWHSSS 2016
CountryKorea, Republic of
CityDaegu
Period16/7/2616/7/30

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Hamiltonian non-displaceability of the Gauss images of isoprametric hypersurfaces (A survey)'. Together they form a unique fingerprint.

Cite this