2021/11/19 by Yu Pan, Pan, Yu, Dan Rutherford +1
Mathematics · #53D42 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2111.10065
openalex publication_date 2021/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Legendrian links and tangles in J1S1 and J1[0,1] equipped with Morse complex families over a field \mathbbF and classify them up to Legendrian cobordism. When the coefficient field is \mathbbF2 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 classification to construct augmented Legendrian surfaces in J1M with dim M = 2 realizing any prescribed monodromy representation, Φ:π1(M,x0) → GL(n, \mathbbF).