Geography of bilinearized Legendrian contact homology

[en] We study the geography of bilinearized Legendrian contact homology for closed connected Legendrian submanifolds with vanishing Maslov class in 1–jet spaces. We show that this invariant detects whether the two augmentations used to define it are DGA homotopic or not. We describe a collection of graded vector spaces containing all possible values for bilinearized Legendrian contact homology and then show that all these vector spaces can be realized.

Disciplines :

Mathematics

Author, co-author :

Bourgeois, Frédéric

Galant, Damien ; Université de Mons - UMONS > Faculté des Sciences > Service d'Analyse numérique

Language :

English

Title :

Geography of bilinearized Legendrian contact homology

Publication date :

09 December 2024

Journal title :

Algebraic and Geometric Topology

ISSN :

1472-2747

eISSN :

1472-2739

Publisher :

Mathematical Sciences Publishers

Volume :

Issue :

Pages :

3571-3604

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://msp.org/agt/2024/24-7/agt-v24-n7-p01-s.pdf

Research unit :

S835 - Analyse numérique

Research institute :

Complexys

Funders :

ANR - Agence Nationale de la Recherche
IUF - Institut Universitaire de France
F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding number :

16-CE40-0017; 15-CE40-0007; 21-CE40-0002

Funding text :

Bourgeois was partially supported by the Institut Universitaire de France and by the ANR projects Quantact (16-CE40-0017), Microlocal (15-CE40-0007) and COSY (21-CE40-0002). Galant is an FRS-FNRS research fellow.

Available on ORBi UMONS :

since 19 December 2024

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Bibliography

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