Semi-global Kuranishi charts and the definition of contact homology

Erkao Bao, Ko Honda

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold (M,ξ) and some auxiliary data D, we define an algebra HC(D). If D1 and D2 are two choices of auxiliary data for (M,ξ), then HC(D1) and HC(D2) are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.

Original languageEnglish (US)
Article number108864
JournalAdvances in Mathematics
Volume414
DOIs
StatePublished - Feb 1 2023

Bibliographical note

Funding Information:
KH supported by NSF Grants DMS-1406564 and DMS-1549147 .

Publisher Copyright:
© 2023

Keywords

  • Contact homology
  • Contact structure
  • Reeb dynamics
  • Symplectic field theory

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