2023/08/05 by Kim, Hyun Kyu
#13F60 #20C35 #20G42 #47B02 #57K20 #57K35 #81R60 #83C45 #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2308.02934
For a punctured surface \mathfrakS, the author and Scarinci (arXiv:2112.13329) have recently constructed a quantization of a moduli space of Lorentzian metrics on the 3-manifold \mathfrakS × ℝ of constant sectional curvature Λ∈ \-1,0,1\. The invariance of this quantization under the action of the mapping class group \rm MCG(\mathfrakS) of \mathfrakS yields families of unitary representations of \rm MCG(\mathfrakS) on a Hilbert space, with key ingredients being three versions of the quantum dilogarithm functions depending on Λ. In this survey article, we review and elaborate on this result.