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 .
Keywords
link concordance, derived series, homology cobordism
