Mathematics Colloquia and Seminars

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Knot invariants are elements of of H^0 (K - D), where K is the space of all maps of the circle into the 3-sphere and D is the subspace of non-embeddings. By "duality" H^0 is intimately related with the homology of D. Vassiliev's spectral sequence arises from a filtration of D given by arranging maps by level of complexity; it yields certain knot invariants of "finite type".

This talk is an introduction to spectral sequences and their use in constructing the finite type invariants. I will focus on explaining the geometric intuition underlying Vassiliev's ideas.