Commensurability of 1-cusped hyperbolic 3-manifolds

Danny Calegari; Nathan M. Dunfield

doi:10.1090/S0002-9947-02-02988-4

Commensurability of 1-cusped hyperbolic 3-manifolds

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

Abstract

We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres where every commensurable knot complement in a homology sphere has non-monic Alexander polynomial.

Original language	English (US)
Pages (from-to)	2955-2969
Number of pages	15
Journal	Transactions of the American Mathematical Society
Volume	354
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9947-02-02988-4
State	Published - 2002
Externally published	Yes

Keywords

Alexander polynomial
Character variety
Commensurability
Virtual Fibration Conjecture

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres where every commensurable knot complement in a homology sphere has non-monic Alexander polynomial.",

keywords = "Alexander polynomial, Character variety, Commensurability, Virtual Fibration Conjecture",

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AB - We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres where every commensurable knot complement in a homology sphere has non-monic Alexander polynomial.

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KW - Character variety

KW - Commensurability

KW - Virtual Fibration Conjecture

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JF - Transactions of the American Mathematical Society

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Commensurability of 1-cusped hyperbolic 3-manifolds

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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