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A4-colored knots and their surgery equivalence
by
Steven D. Wallace
Louisiana State University
The pair (K, r) consisting of a knot in the three-sphere and a representation of the knot group onto the alternating group on four letters is said to be an A4-colored knot. We establish lower and upper bounds for the number of equivalence classes of A4-colored knots up to surgery along unknots representing elements in the kernel of r. Such surgeries preserve A4-colorability. We do this by defining a complete invariant for A4-colored surgery equivalence. Indeed, this is an analog to the classical result that every knot has a "surgery description" or equivalently that every knot is surgery equivalent to the unknot if we place fewer restrictions on the allowed surgery curves.
Date received: March 5, 2008
Copyright © 2008 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cawt-06.