Homology and Derived Series of Groups II: Dwyer's Theorem

Details Homology and Derived Series of Groups II: Dwyer's Theorem Homology and Derived Series of Groups II: Dwyer's Theorem

2006-09-18

arxiv.org/abs/math/0609484v3

Geometry and Topology,12, (2008) 199-232

Mathematics

Geometric Topology

26 pages. In this version, we have included a new proof of part of the main theorem. The new proof is somewhat simpler and sta

Scientific paper

We give new information about the relationship between the low-dimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group. Applications are given to detecting when a set of elements of a group generates a subgroup ``large enough'' to map onto a non-abelian free solvable group, and to concordance and grope cobordism of links. We also greatly generalize several key homological results employed in recent work of Cochran-Orr-Teichner, in the context of classical knot concordance. In 1963 J. Stallings established a strong relationship between the low-dimensional homology of a group and its lower central series quotients. In 1975 W. Dwyer extended Stallings' theorem by weakening the hypothesis on the second homology groups. The naive analogues of these theorems for the derived series are false. In 2003 the second author introduced a new characteristic series, associated to the derived series, called the torsion-free derived series. The authors previously established a precise analogue, for the torsion-free derived series, of Stallings' theorem. Here our main result is the analogue of Dwyer's theorem for the torsion-free derived series. We also prove a version of Dwyer's theorem for the rational lower central series. We apply these to give new results on the Cochran-Orr-Teichner filtration of the classical link concordance group.

Affiliated with

Also associated with

No associations

Rating

Homology and Derived Series of Groups II: Dwyer's Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homology and Derived Series of Groups II: Dwyer's Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homology and Derived Series of Groups II: Dwyer's Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-648320