Twisted Iwasawa invariants of knots

Ryoto Tange and Jun Ueki

Mathematische Nachrichten, 2024, vol. 297, issue 4, 1519-1534

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.

Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200543

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:4:p:1519-1534

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().