2012/12/31 by Nitu Kitchloo, Kitchloo, Nitu, Jack Morava +1
Mathematics · Physics and Astronomy · #19D55 #53D12 #53D55 #55N35 #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.AT #math.KT #math.MP #math.SG #msc:19D55 #msc:53D12 #msc:53D55 #msc:55N35
paper · pdf · doi:10.48550/arxiv.1212.6905
The paper has been largely reorganized to interpret the action of the Grothendieck--Teichmüller group in the context of a conjecture of Kontsevich. The title has been changed accordingly. The section on the Waldhausen K-theory of $sΩ$ has been removed and will form part of a separate document. All other sections have been preserved
arxiv created 2015/10/31 · arxiv updated 2015/11/03
We consider an oriented version of the stable symplectic category defined in \citeN. We show that the group of monoidal automorphisms of this category, that fix each object, contains a natural subgroup isomorphic to the solvable quotient (or a graded-abelian quotient) of the Grothendieck--Teichmüller group. This establishes a stable version of a conjecture of Kontsevich which states that groups closely related to the Grothendieck--Teichmüller group act on the moduli space of certain field theories \citeKO. The above quotient of the Grothendieck--Teichmüller group is also shown to be the motivic group of monoidal automorphisms of a canonical representation (or fiber functor) on the stable symplectic category.