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Some prospects with the splicing operad

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HHHW04 - Manifolds

Roughly six years ago I described an operad that acts on spaces of `long knots'. This is the space of smooth embeddings of Rj into Rn. The embeddings are required to be standard (linear) outside of a disc, and come equipped with a trivialisation of their normal bundles. This splicing operad gives a remarkably compact description of the homotopy-type of the space of classical long knots (j=1, n=3), that meshes well with the machinery of 3-manifold theory: JSJ -decompositions and geometrization. What remains to be seen is how useful this splicing operad might be when n is larger than 3. I will talk about what is known at present, and natural avenues to explore.

This talk is part of the Isaac Newton Institute Seminar Series series.

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