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A Homological Approach to Relative Knot Invariants

2009/09/23 by Georgi D. Gospodinov, Gospodinov, Georgi D.
Computer Science · Mathematics · #57M27 #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis #math.SG #msc:57M27

paper · pdf · doi:10.48550/arxiv.0909.4316

arxiv created 2009/09/23 · openalex publication_date 2009/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define relative versions of the classical invariants of Legendrian and transverse knots in contact 3-manifolds for knots that are homologous to a fixed reference knot. We show these invariants are well-defined and give some basic properties.

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