Coherent orientations in symplectic field theory revisited

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Abstract

In symplectic field theory (SFT), the moduli spaces of J-holomorphic curves can be oriented coherently (i.e., in a manner compatible with gluing). In this note, we correct the signs involved in the generating function H in SFT so that the master equation H· H= 0 holds assuming transversality. The orientation convention that we use is consistent with that of Hutchings–Taubes from (J Symplectic Geom 7(1):29–133, 2009), but differs from that of Bourgeois–Mohnke in (Math Z 248(1):123–146, 2004).

Original languageEnglish (US)
Article number30
JournalMathematische Zeitschrift
Volume305
Issue number2
DOIs
StatePublished - Oct 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • Coherent orientation
  • Contact homology
  • Contact structure
  • Symplectic field theory

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