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Jonathan Hanselman : Satellite knots and immersed curves

Satellite operations are an valuable method of constructing complicated knots from simpler ones, and much work has gone into understanding how knot invariants change under these operations. We describe a new way of computing the (UV=0 quotient of the) knot Floer complex using an immersed Heegaard diagram obtained from a Heegaard diagram for the pattern and the immersed curve representing the knot Floer complex of the companion. This is particularly useful for (1,1)-patterns, since in this case the resulting immersed diagram is genus one. In some cases the immersed curve representing the satellite knot Floer complex can be obtained directly by deforming the diagram, generalizing earlier work with Watson on cables. This is joint work with Wenzhao Chen.

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