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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Abstract
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 |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Powell, Professor 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: | 1472-2747 |
| ISSN (Online): | 1472-2739 |
| Published Online: | 08 April 2012 |
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