4,190 research outputs found
Twisted Alexander Invariants of Twisted Links
Let L be an oriented (d+1)-component link in the 3-sphere, and let L(q) be
the d-component link in a homology 3-sphere that results from performing
1/q-surgery on the last component. Results about the Alexander polynomial and
twisted Alexander polynomials of L(q) corresponding to finite-image
representations are obtained. The behavior of the invariants as q increases
without bound is described.Comment: 21 pages, 6 figure
Twisted Alexander Polynomials and Representation Shifts
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 image of the commutator subgroup of the knot group.Comment: 7 pages, no figure
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