A second order algebraic knot concordance group

Powell, M. (2012) A second order algebraic knot concordance group. Algebraic and Geometric Topology, 12(2), pp. 685-751. (doi: 10.2140/agt.2012.12.685)

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Let C be the topological knot concordance group of knots S 1 ⊂ S 3 under connected sum modulo slice knots. Cochran, Orr and Teichner defined a filtration: C ⊃ F (0) ⊃ F (0.5) ⊃ F (1) ⊃ F (1.5) ⊃ F (2) ⊃ ... 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 AC 2, our second order algebraic knot concordance group. We define a group homomorphism C → AC 2 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 AC 2. Moreover there is a surjective homomorphism AC 2 → C/F (0.5), and we show that the kernel of this homomorphism is nontrivial.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Algebraic and Geometric Topology
Publisher:Mathematical Sciences Publishers
ISSN (Online):1472-2739
Published Online:08 April 2012
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