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Sean Tilson (Bergische Universität Wuppertal): Squaring operations in the Motivic and C_2-equivariant Adams spectral sequence.
May 16th, 2017


Multiplicative structure and power operations have been used to great effect in many familiar spectral sequences. One main application is an easy proof of the collapse of a spectral sequence or a computation of the multiplicative structure or power operations on the target of a spectral sequence. In the case of the Adams spectral sequence one can do more. In his thesis, Bruner gave definitive formulas for differentials in the Adams spectral sequence of an highly structured ring spectrum. In particular, this gives a nice intuitive explanation of the Hopf invariant one differential d_2(h_{i+1})=h_0h_i^2. In explaining this differential, we will expose the moving parts of such a result. We will also present a motivic (over the real and complex numbers) and C_2-equivariant version of Bruner's results in the case of permanent cycles.

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