A Second Order Algebraic Knot Concordance Group

2011/09/04 by Mark Powell, Powell, Mark
Mathematics · Medicine · #55U15 #57M10 #57M25 #57M27 #57N70 (Primary) 57M05 #57P10 (Secondary) #57R65 #57R67 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1109.0761

openalex publication_date 2011/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an algebraic group comprising symmetric chain complexes which captures the first two stages of the Cochran-Orr-Teichner solvable filtration of the knot concordance group in a single obstruction. To achieve this we impose additional structure on each chain complex which puts extra control on the fundamental groups, and in particular on the way in which they can change in a concordance.

Related

• The Non-triviality of the Grope Filtrations of The Knot and Link Concordance Groups
• Order 2 Algebraically Slice Knots
• A survey of classical knot concordance
• Obstructing two-torsion in the rational knot concordance group
• Algebraic concordance groups for links