Geometric criteria for overtwistedness

Roger Casals, Emmy Murphy, Francisco Presas

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


In this article we establish efficient geometric criteria to decide whether a contact manifold is overtwisted. Starting with the original definition, we first relate overtwisted disks in different dimensions and show that a manifold is overtwisted if and only if the Legendrian unknot admits a loose chart. Then we characterize overtwistedness in terms of the monodromy of open book decompositions and contact surgeries. Finally, we provide several applications of these geometric criteria.

Original languageEnglish (US)
Pages (from-to)563-604
Number of pages42
JournalJournal of the American Mathematical Society
Issue number2
StatePublished - Apr 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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