Maslov index, Lagrangians, mapping class groups and TQFT (Q2855509)

The paper under review studies certain central extensions of the mapping class group \(\Gamma_g\) of a closed surface of genus \(g\), which are used for resolving so-called anomalies which arise in topological quantum field theories. The extended mapping class group \(\widetilde{\Gamma}_g\) is a central extension of \(\Gamma_g\), with the multiplication given by the Maslov cocycle, which arises from topological quantum field theory and is related to the signature cocycle.NEWLINENEWLINEThe authors obtain explicit formulas for computing products of certain lifts of Dehn twists to \(\widetilde{\Gamma}_g\). They define a certain subgroup \(\widetilde{\Gamma}_g^{++}\) of \(\widetilde{\Gamma}_g\) as the subgroup generated by these lifts of Dehn twists, and they show that it has index four inside of \(\widetilde{\Gamma}_g\). The authors use and clarify ideas due to Walker in their analysis.