# Introduction to quantum representations of mapping class groups

## TL;DR

This paper offers an accessible, skein-theory-based construction of Witten-Reshetikhin-Turaev representations of the mapping class group, detailing their properties such as Hermitian structure and irreducibility.

## Contribution

It provides a self-contained, skein-theoretic approach to constructing quantum representations of the mapping class group, avoiding surgery techniques and making the topic more accessible.

## Key findings

- Construction relies solely on skein theory (Kauffman Bracket)
- Properties include Hermitian structure, irreducibility, and integrality at prime level
- Accessible to non-specialists

## Abstract

We provide an (almost) self-contained construction of the Witten-Reshetikhin-Turaev representations of the mapping class group. We describe its properties including its Hermitian structure, irreducibility and integrality (at prime level). The construction of these notes relies only on skein theory (Kauffman Bracket) and does not use surgery techniques. We hope that they will be accessible to non-specialists.