Geometry & Topology
- Geom. Topol.
- Volume 12, Number 1 (2008), 387-430.
Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group
For any group G, we define a new characteristic series related to the derived series, that we call the torsion-free derived series of G. Using this series and the Cheeger–Gromov –invariant, we obtain new real-valued homology cobordism invariants for closed –dimensional manifolds. For –dimensional manifolds, we show that is a linearly independent set and for each , the image of is an infinitely generated and dense subset of .
In their seminal work on knot concordance, T Cochran, K Orr and P Teichner define a filtration of the –component (string) link concordance group, called the –solvable filtration. They also define a grope filtration . We show that vanishes for –solvable links. Using this, and the nontriviality of , we show that for each , the successive quotients of the –solvable filtration of the link concordance group contain an infinitely generated subgroup. We also establish a similar result for the grope filtration. We remark that for knots (), the successive quotients of the –solvable filtration are known to be infinite. However, for knots, it is unknown if these quotients have infinite rank when .
Geom. Topol., Volume 12, Number 1 (2008), 387-430.
Received: 9 April 2007
Revised: 2 September 2007
Accepted: 15 November 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 20F14: Derived series, central series, and generalizations
Harvey, Shelly L. Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group. Geom. Topol. 12 (2008), no. 1, 387--430. doi:10.2140/gt.2008.12.387. https://projecteuclid.org/euclid.gt/1513800023