Report
Iterated satellite operators on the knot concordance group
| العنوان: | Iterated satellite operators on the knot concordance group |
|---|---|
| المؤلفون: | Cha, Jae Choon, Kim, Taehee |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, 57K10, 57N70 |
| الوصف: | 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 Pinz\'{o}n-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. Comment: 32 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.04629 |
| رقم الانضمام: | edsarx.2402.04629 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |