Braids

Everyone intuitively understands the concept of a braid as a collection of intertwined strands. However, mathematically braids have a simple algebraic description in terms of a group. This group structure also connects them to the mapping class groups of a surface: each element of this group describes a way of mapping a surface to itself. In this course I will present the basic theory of braids, assuming relatively few prerequisites. There will be a blend of algebra (mainly group theory) and algebraic topology (no prior knowledge assumed). Topics likely to be covered include:

• Definition of braids
• Artin Braid Groups
• Fundamental Groups & Configuration spaces
• The Presentation Theorem
• Representations of the braid group