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
Powell, Mark 1
@article{10_2140_agt_2012_12_685,
author = {Powell, Mark},
title = {A second order algebraic knot concordance group},
journal = {Algebraic and Geometric Topology},
pages = {685--751},
year = {2012},
volume = {12},
number = {2},
doi = {10.2140/agt.2012.12.685},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.685/}
}
Powell, Mark. A second order algebraic knot concordance group. Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 685-751. doi: 10.2140/agt.2012.12.685
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