Geoffroy Horel: Galois group and space of knots

Abstract: Goodwillie and Weiss introduced a method to study embedding spaces called manifold calculus. When specialized to the case of knots, this theory produces a tower of approximations that are related to finite type invariants of knots à la Vassiliev. From this tower, one can construct a spectral sequence, whose E1-page consists of homotopy groups of spheres and which converges to an approximation of the space of knots. In recent work with Pedro Boavida de Brito, we construct an
interesting action of the absolute Galois group of the rationals on this tower. This action implies some vanishing results on the differentials of this spectral sequence.