Iterated satellite operators on the knot concordance group
arxiv(2024)
Abstract
We show that for a winding number zero satellite operator P on the knot
concordance group, if the axis of P has nontrivial self-pairing under the
Blanchfield form of the pattern, then the image of the iteration P^n
generates an infinite rank subgroup for each n. Furthermore, the graded
quotients of the filtration of the knot concordance group associated with P
have infinite rank at all levels. This gives an affirmative answer to a
question of Hedden and Pinzón-Caicedo in many cases. We also show that
under the same hypotheses, P^n is not a homomorphism on the knot concordance
group for each n. We use amenable L^2-signatures to prove these results.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined