λ→0 limit of 2+1 quantum gravity for arbitrary genus

The abstract quantum algebra of observables for 2+1 gravity is analysed in the limit of small cosmological constant. The algebra splits into two sets with an explicit phase space representation; one set consists of 6g–6 commuting elements which form a basis for an algebraic manifold defined by the trace and rank identities; the other set consists of 6g–6 tangent vectors to this manifold. The action of the quantum mapping class group leaves the algebra and algebraic manifold invariant. The previously presented representation for g=2 is analysed in this limit and reduced to a very simple form. The symplectic form for g=2 is computed.