Braids and Dynamics

“This book is laudable for giving an account of the theory of braid groups and surface homeomorphisms that's down-to-earth, inviting, and accessible to its intended audience: beginning graduate students, advanced undergraduates, and applied mathematicians.” (Bena Tshishiku, Mathematical Reviews, February, 2024)“This book is a very pleasant to read, linking seemingly unrelated topic like braid and fluid dynamics, perhaps a bit easier for a pure mathematician than for an applied one, but still very much enjoyable.” (Mauro Artigiani, zbMATH 1509.37003, 2023)“This short book considers an unusual combination of algebraic topology, dynamics and applications to the mixing of fluids. Probably not many mathematics texts use a taffy puller in a primary example. This one does, and it incorporates interesting connections to dynamics on surfaces, the algebraic topology of braids and applications to mixing. … Several intriguing ideas are presented here very quickly, and it takes some effort to make all the pieces fit together.” (Bill Satzer, MAA Reviews, January 29, 2023)

• Introduction.- Topological dynamics on the torus.- Stretching with three rods.- Braids.- The Thurston-Nielsen classification.- Topological entropy.- Train tracks.- Dynnikov coordinates.- The braidlab library.- Braids and data analysis.- References.- Appendix: Derivation of Dynnikov update rules.