I am looking for an introduction of Quantum Geometry (math-subject) for mathematicians. This paper presents a survey however I am looking for something with more mathematical depth and motivation (for a no-physicist). Something like the book Quantum Geometry: A Framework for Quantum General Relativity but for mathematicians.
Just to be clear: I am aware of the these questions on quantum physics for mathematicians and this question on quantum mechanics. I am asking for a specific kind of geometry (quantum geometry) from the perspective of geometry (mathematics). This is not a general question asking about the geometry used in quantum physics.