Fox formulas for twisted Alexander invariants associated to representations of knot groups over rings of S-integers

Ryoto Tange

doi:10.1142/S0218216518500335

Fox formulas for twisted Alexander invariants associated to representations of knot groups over rings of S-integers

Ryoto Tange

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We present a generalization of the Fox formula for twisted Alexander invariants associated to representations of knot groups over rings of S-integers of F, where S is a finite set of finite primes of a number field F. As an application, we give the asymptotic growth of twisted homology groups.

Original language	English
Article number	1850033
Journal	Journal of Knot Theory and its Ramifications
Volume	27
Issue number	5
DOIs	https://doi.org/10.1142/S0218216518500335
Publication status	Published - 2018 Apr 1
Externally published	Yes

Keywords

arithmetic topology
Knot
Mahler measure
twisted Alexander invariant

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216518500335

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title = "Fox formulas for twisted Alexander invariants associated to representations of knot groups over rings of S-integers",

abstract = "We present a generalization of the Fox formula for twisted Alexander invariants associated to representations of knot groups over rings of S-integers of F, where S is a finite set of finite primes of a number field F. As an application, we give the asymptotic growth of twisted homology groups.",

keywords = "arithmetic topology, Knot, Mahler measure, twisted Alexander invariant",

author = "Ryoto Tange",

note = "Funding Information: The author would like to thank Masanori Morishita for suggesting him an interesting problem, Jun Ueki for helpful discussions and suggesting references, and Daniel S. Silver for helpful communications. The author is partially supported by Grant-in-Aid for JSPS Fellow 16J03575.",

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AU - Tange, Ryoto

N1 - Funding Information: The author would like to thank Masanori Morishita for suggesting him an interesting problem, Jun Ueki for helpful discussions and suggesting references, and Daniel S. Silver for helpful communications. The author is partially supported by Grant-in-Aid for JSPS Fellow 16J03575.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We present a generalization of the Fox formula for twisted Alexander invariants associated to representations of knot groups over rings of S-integers of F, where S is a finite set of finite primes of a number field F. As an application, we give the asymptotic growth of twisted homology groups.

AB - We present a generalization of the Fox formula for twisted Alexander invariants associated to representations of knot groups over rings of S-integers of F, where S is a finite set of finite primes of a number field F. As an application, we give the asymptotic growth of twisted homology groups.

KW - arithmetic topology

KW - Knot

KW - Mahler measure

KW - twisted Alexander invariant

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