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- Title
Twisted Iwasawa invariants of knots.
- Authors
Tange, Ryoto; Ueki, Jun
- Abstract
Let p$p$ be a prime number and m$m$ an integer coprime to p$p$. In the spirit of arithmetic topology, we introduce the notions of the twisted Iwasawa invariants λ,μ,ν$\lambda , \mu , \nu$ of GLN${\rm GL}_N$‐representations and Z/mZ×Zp${\mathbb {Z}}/m{\mathbb {Z}}\times {\mathbb {Z}}_{p}$‐covers of knots. We prove among other things that the set of Iwasawa invariants determines the genus and the fiberedness of a knot, yielding their profinite rigidity. Several intuitive examples are attached. We further prove the μ=0$\mu =0$ theorem for SL2${\rm SL}_2$‐representations of twist knot groups and give some remarks.
- Subjects
PRIME numbers; KNOT theory; ARITHMETIC; TOPOLOGY; INTEGERS
- Publication
Mathematische Nachrichten, 2024, Vol 297, Issue 4, p1519
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202200543