$\La \to 0$ limit of 2+1 Quantum Gravity for arbitrary genus

Abstract

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 $6g-6$ {\it 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.

13 pages plain TEX, extra comments and references added

References in corpus (5)

• Invariants of 2+1 Quantum Gravity
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• New Loop Representations for 2+1 Gravity
• Equivalent Quantisations of (2+1)-Dimensional Gravity
• Quantisation of 2+1 gravity for genus 2