Twisted Alexander polynomials and surjectivity of a group homomorphism
نویسندگان
چکیده
منابع مشابه
Twisted Alexander polynomials and surjectivity of a group homomorphism
If ϕ : G → G ′ is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G ′. As an application, we show non-existence of surjective homomorphism between certain knot groups.
متن کاملTwisted Alexander Polynomial and Surjectivity of a Group Homomorphism
If φ : G → G is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G. As an application, we show non-existence of surjective homomorphism between certain knot groups.
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X.S. Lin’s original definition of twisted Alexander knot polynomial is generalized for arbitrary finitely presented groups. J. Cha’s fibering obstruction theorem is generalized. The group of a nontrivial virtual knot shown by L. Kauffman to have trivial Jones polynomial is seen also to have a faithful representation that yields a trivial twisted Alexander polynomial.
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For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot group admits a finite-image representation such that the image of the fundamental group of an incompressible Seifert surface is a proper subgroup of the ima...
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We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2,C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. ...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2005
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2005.5.1315