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1. Scissors Congruence


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      Problem 1.1.

      Consider the sequence $$0\to \mathcal{P}(E^2) \xrightarrow{prism} \mathcal{P}(E^3)\to \R\otimes \R/\Z \to \Omega^1 \R/\Z\to 0,$$ which is known to be exact. There are two known proofs: one uses homological methods (Dupont), the other uses more elementary methods (Jessen). How do they relate to each other?


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          Problem 1.2.

          Is the map from Goncahrov’s projectivised scissors congruence groups to the Hopf algebra of polylogarithms surjective?
            1. Remark. [Daniil Rudenko] This is a warm-up to investigating if this map is an isomorphism (i.e. injective + surjective). Also, worth asking what this means for higher scissors congruence.


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                  Problem 1.3.

                  There are two different spectral sequences arising from Sah & Goncharov; what is their relationship? Relation to the Minkowski Filtration?
                    1. Remark. [Cary Malkiewich] Another way of saying this is: how does the filtration of the Tits complex that arises from the dimensions of the subspaces interact with the filtration that arises from the Dehn invariant coproduct maps?

                          Cite this as: AimPL: Scissors congruences, algebraic K-theory and Steinberg modules, available at http://aimpl.org/scissorssteinberg.