THE BETTI SIDE OF THE DOUBLE SHUFFLE THEORY: A SURVEY (Various aspects of multiple zeta values)

This is a survey of [EFl, EF2, EF3]. The purpose of this series of papers is: (1) to give a proof that associator relations imply double shuffie relations, alternative to [F3]; (2) to make explicit the bitorsor structure on Racinet's torsor of double shuffie relations. The main tool is the interpretation of the harmonic coproduct in terms of the topology of the moduli spaceM0, 4andM0, 5, introduced in [DeT], and its extension to the Betti setup