We describe a theory of finite type invariants for null-homologous knots in rational homology 3-spheres which can be thought of as a rational homology version of the theory studied by Garoufalidis and Kricker for knots in integral homology 3-spheres. We study the graded space $\mathcal{G}$ associated to this theory, whose dual space is the space of rational valued finite type invariants, graded by the degree. We introduce a graded diagram space $\mathcal A$ and a surjection $\mathcal A\twoheadrightarrow\mathcal G$, which we conjecture to be an isomorphism. Two universal invariants play an important role in this theory, namely the Kricker lift of the Kontsevich integral and the Lescop invariant constructed by means of equivariant intersections in configuration spaces.

Zoom meeting ID: 919-9946-8404

Password: see email announcement or contact the seminar organisers:

Tobias Barthel (barthel.tobi[at]gmail.com)

David Gay (dgay[at]uga.edu)

Arunima Ray (aruray[at]mpim-bonn.mpg.de)

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