# Geography of bilinearized Legendrian contact homology

## TL;DR

This paper investigates the bilinearized Legendrian contact homology of Legendrian submanifolds, demonstrating its ability to distinguish augmentation homotopy classes and characterizing all possible invariant values.

## Contribution

It introduces a comprehensive description of the invariant's possible values and proves their realizability, advancing understanding of Legendrian contact homology in 1-jet spaces.

## Key findings

- Invariant detects augmentation homotopy classes
- All possible graded vector spaces are characterized
- Realizability of all invariant values is established

## Abstract

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.