2008/07/31 by Dmitry Fuchs, Dan Rutherford · 3 citations
Computer Science · Mathematics · #Algebra over a field #Combinatorics #Duality (order theory) #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Mathematics #Pure mathematics #Topological and Geometric Data Analysis #math.GT #math.SG #msc:57M27 #msc:57R17
paper · pdf · doi:10.1112/jtopol/jtq033
Revised version, to appear in Journal of Topology. Following referee suggestions, parts of sections 4 and 6 have been removed for more efficient exposition
arxiv created 2010/12/08 · openalex publication_date 2011/01/01 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that if a Legendrian knot in a standard contact space ℝ3 possesses a generating family, then there exists an augmentation of the Chekanov–Eliashberg differential graded algebra so that the associated linearized contact homology (LCH) is isomorphic to singular homology groups arising from the generating family. In this setting, we show that Sabloff's duality result for LCH may be viewed as Alexander duality. In addition, we provide an explicit construction of a generating family for a front diagram with graded normal ruling and give a new approach to augmentation implies normal ruling.