# Augmented Legendrian cobordism in $J^1S^1$

@inproceedings{Pan2021AugmentedLC, title={Augmented Legendrian cobordism in \$J^1S^1\$}, author={Yu Pan and Dan Rutherford}, year={2021} }

We consider Legendrian links and tangles in JS and J[0, 1] equipped with Morse complex families over a field F and classify them up to Legendrian cobordism. When the coefficient field is F2 this provides a cobordism classification for Legendrians equipped with augmentations of the Legendrian contact homology DG-algebras. A complete set of invariants, for which arbitrary values may be obtained, is provided by the fiber cohomology, a graded monodromy matrix, and a mod 2 spin number. We apply the…

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