Algebraic & Geometric Topology 12 (2012) 685–751

DOI: 10.2140/agt.2012.12.685

Abstract

Let C be the topological knot concordance group of knots S¹ ⊂ S³ under connected sum modulo slice knots. Cochran, Orr and Teichner defined a filtration:

The quotient C ∕ F_(0.5) is isomorphic to Levine’s algebraic concordance group; F_(0.5) is the algebraically slice knots. The quotient C ∕ F_(1.5) contains all metabelian concordance obstructions.

Using chain complexes with a Poincaré duality structure, we define an abelian group  AC₂, our second order algebraic knot concordance group. We define a group homomorphism C→AC₂ which factors through C ∕ F_(1.5), and we can extract the two stage Cochran–Orr–Teichner obstruction theory from our single stage obstruction group AC₂. Moreover there is a surjective homomorphism AC₂ →C ∕ F_(0.5), and we show that the kernel of this homomorphism is nontrivial.

Keywords

knot concordance group, solvable filtration, symmetric chain complex

Mathematical Subject Classification

Primary: 57M25, 57M27, 57N70, 57R67

Secondary: 57M10, 57R65

References

Publication

Received: 29 November 2011
Revised: 11 January 2012
Accepted: 13 January 2012
Published: 8 April 2012

Authors