Selective symplectic homology with applications to contact non-squeezing

Igor Uljarević*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove a contact non-squeezing phenomenon on homotopy spheres that are fillable by Liouville domains with large symplectic homology: there exists a smoothly embedded ball in such a sphere that cannot be made arbitrarily small by a contact isotopy. These homotopy spheres include examples that are diffeomorphic to standard spheres and whose contact structures are homotopic to standard contact structures. As the main tool, we construct a new version of symplectic homology, called selective symplectic homology, that is associated to a Liouville domain and an open subset of its boundary. The selective symplectic homology is obtained as the direct limit of Floer homology groups for Hamiltonians whose slopes tend to on the open subset but remain close to and positive on the rest of the boundary.

Original languageEnglish
Pages (from-to)2458-2482
Number of pages25
JournalCompositio Mathematica
Issue number11
StatePublished - 18 Sep 2023
Externally publishedYes


  • contact Floer homology
  • contact non-squeezing
  • symplectic homology


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