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Commensurability of 1-cusped hyperbolic 3-manifolds

Author(s): Danny Calegari; Nathan M. Dunfield
Journal: Trans. Amer. Math. Soc. 354 (2002), 2955-2969.
MSC (2000): Primary 57M25, 57M50
Posted: February 25, 2002
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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.

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Additional Information:

Danny Calegari
Affiliation: Department of Mathematics, Harvard University, Cambridge Massachusetts 02138
Email: dannyc@math.harvard.edu

Nathan M. Dunfield
Affiliation: Department of Mathematics, Harvard University, Cambridge Massachusetts 02138
Email: nathand@math.harvard.edu

DOI: 10.1090/S0002-9947-02-02988-4
PII: S 0002-9947(02)02988-4
Keywords: Virtual Fibration Conjecture, commensurability, Alexander polynomial, character variety
Received by editor(s): February 7, 2001
Received by editor(s) in revised form: August 25, 2001
Posted: February 25, 2002
Additional Notes: Both authors were partially supported by the National Science Foundation.
Copyright of article: Copyright 2002, American Mathematical Society

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