On torsion in (bi)linearized Legendrian contact homology in dimension 3

Abstract

Linearized Legendrian contact homology (LCH) and bilinearized LCH are important homological invariants for Legendrian submanifolds in contact geometry. For legendrian knots in $\mathbb{R}^3$, very little was previously known about the possibility of having torsion in these invariants when they are defined over integer coefficients. In this paper, we give properties of torsion that can appear in linearized LCH with integer coefficients, and also give the full geography of bilinearized LCH with integer coefficients.