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2012 A second order algebraic knot concordance group
Mark Powell
Algebr. Geom. Topol. 12(2): 685-751 (2012). DOI: 10.2140/agt.2012.12.685

Abstract

Let C be the topological knot concordance group of knots S1S3 under connected sum modulo slice knots. Cochran, Orr and Teichner defined a filtration:

C ( 0 ) ( 0 . 5 ) ( 1 ) ( 1 . 5 ) ( 2 )

The quotient C(0.5) is isomorphic to Levine’s algebraic concordance group; (0.5) is the algebraically slice knots. The quotient C(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 CAC2 which factors through C(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 AC2C(0.5), and we show that the kernel of this homomorphism is nontrivial.

Citation

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Mark Powell. "A second order algebraic knot concordance group." Algebr. Geom. Topol. 12 (2) 685 - 751, 2012. https://doi.org/10.2140/agt.2012.12.685

Information

Received: 29 November 2011; Revised: 11 January 2012; Accepted: 13 January 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1244.57023
MathSciNet: MR2914616
Digital Object Identifier: 10.2140/agt.2012.12.685

Subjects:
Primary: 57M25, 57M27, 57N70, 57R67
Secondary: 57M10, 57R65

Rights: Copyright © 2012 Mathematical Sciences Publishers

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