Some quantitative results in C0 symplectic geometry

Lev Buhovsky, Emmanuel Opshtein

Research output: Contribution to journalArticlepeer-review


This paper proceeds with the study of the C0-symplectic geometry of smooth submanifolds, as initiated in Humilière et al. (Duke Math J 164(4), 767–799, 2015) and Opshtein (Ann Sci Éc Norm Supér 42(5), 857–864, 2009), with the main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic homeomorphism may preserve and squeeze codimension 4 symplectic submanifolds (C0-flexibility), while this is impossible for codimension 2 symplectic submanifolds (C0-rigidity). We also discuss C0-invariants of coistropic and Lagrangian submanifolds, proving some rigidity results and formulating some conjectures. We finally formulate an Eliashberg-Gromov C0-rigidity type question for submanifolds, which we solve in many cases. Our main technical tool is a quantitative h-principle result in symplectic geometry.

Original languageEnglish
Pages (from-to)1-56
Number of pages56
JournalInventiones Mathematicae
Issue number1
StatePublished - 1 Jul 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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