Iain R. Aitchison

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We characterise the cabling operations on the weight systems of finite type knot invariants. The eigenvectors and eigenvalues of this family of operations are described. The canonical deframing projection for these knot invariants is described over the cable eigenbasis. The action of immanent weight systems on general Feyn-man diagrams is considered, and(More)
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A combinatorial condition is obtained for when immersed or embedded incompressible surfaces in compact 3–manifolds with tori boundary components remain incompressible after Dehn surgery. A combinatorial characterisation of hierarchies is described. A new proof is given of the topological rigidity theorem of Hass and Scott for 3–manifolds containing immersed(More)
It is known that about 70% of surgeries on the figure 8 knot give manifolds which contain immersed incompressible surfaces. We improve this to about 80% by giving a very simple proof that all even surgeries give manifolds containing such a surface. Moreover, we give a quick proof that every (6k, t) surgery is virtually Haken, thereby partially dealing with(More)
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