Braid groups, introduced by Emil Artin in 1925, are mathematical structures that describe the motion of intertwining strands. These braids can be defined from geometric, topological, and algebraic perspectives. Braid theory has played a fundamental role in various areas of mathematics, including knot theory and topological dynamics.
The study of braids in surface dynamics began in the early 1980s and has been developed to an extensive area in the theory of low-dimensional dynamical systems. Specifically, braids serve as invariants that capture the topological behavior of periodic orbits in the context of surface homeomorphisms.
This talk will provide an introduction to braid group theory and its applications in topological dynamics, with a particular focus on examining the periodic orbit structure of iterated homeomorphisms on surfaces.
