Publications [#360673] of Richard Hain

Papers Published

1. Hain, R, Hodge theory of the Turaev cobracket and the Kashiwara-Vergne problem, Journal of the European Mathematical Society, vol. 23 no. 12 (January, 2021), pp. 3889-3933 [doi]
   (last updated on 2024/04/24)

   Abstract:
   In this paper we show that, after completing in the I -adic topology, the Turaev cobracket on the vector space freely generated by the closed geodesics on a smooth, complex algebraic curve X with a quasi-algebraic framing is a morphism of mixed Hodge structure. We combine this with results of a previous paper on the Goldman bracket to construct torsors of solutions to the Kashiwara-Vergne problem in all genera. The solutions so constructed form a torsor under a prounipotent group that depends only on the topology of the framed surface. We give a partial presentation of these groups. Along the way, we give a homological description of the Turaev cobracket.