We consider Legendrian links and tangles in and equipped with Morse complex families over a field and classify them up to Legendrian cobordism. When the coefficient field is , 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 spin number. We apply the classification to construct augmented Legendrian surfaces in with realizing any prescribed monodromy representation, .
Cite this article
Yu Pan, Dan Rutherford, Augmented Legendrian cobordism in . Quantum Topol. 14 (2023), no. 3, pp. 533–600DOI 10.4171/QT/195