Central Extension of Mapping Class Group via Chekhov-Fock Quantization

TL;DR

This paper investigates the central extension of mapping class groups in the context of Chekhov-Fock quantization, revealing its relation to known classes and confirming consistency with Kashaev quantization.

Contribution

It identifies the specific form of the central extension in Chekhov-Fock quantization and its relation to the Meyer and Euler classes, linking it to Kashaev quantization.

Findings

Central extension is 12 times the Meyer class plus puncture Euler classes.

Extension matches the one in Kashaev quantization.

Provides a precise algebraic description of the extension.

Abstract

The central extension of mapping class groups of punctured surfaces of finite type that arises in Chekhov-Fock quantization is 12 times of the Meyer class plus the Euler classes of the punctures, which agree with the one arising in the Kashaev quantization.