An analog of a modular functor from quantized Teichm"uller theory

TL;DR

This paper demonstrates that quantized Teichmüller spaces exhibit factorization properties similar to those needed for a modular functor, bridging concepts in quantum topology and mathematical physics.

Contribution

It introduces an analog of a modular functor derived from the properties of quantized Teichmüller spaces, expanding the mathematical framework.

Findings

Quantized Teichmüller spaces have modular functor-like factorization properties.

Establishes a new connection between quantum topology and modular functors.

Provides foundational insights for future research in quantum geometry.

Abstract

It is shown that the quantized Teichm"uller spaces have factorization properties like those required in the definition of a modular functor.