This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly simplifies arguments and also allows us to show that there exist Legendrian links with infinitely many nonorientable exact Lagrangian fillings.
Augmentations and immersed Lagrangian fillings
For a Legendrian link with or , immersed exact Lagrangian fillings of can be lifted to conical Legendrian fillings of . When is embedded, using the version of functoriality for Legendrian contact homology (LCH) from Pan and Rutherford [J. Symplectic Geom.
- NSF-PAR ID:
- 10420619
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Journal of Topology
- Volume:
- 16
- Issue:
- 1
- ISSN:
- 1753-8416
- Page Range / eLocation ID:
- p. 368-429
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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