T-homogeneous braids and braided open books

Braids can be interpreted as loops in certain spaces of complex polynomials. In this talk I will discuss how this point of view leads to the definition of the concept of a braided open book decomposition of the 3-sphere. It is not known if every open book can be braided in this way, but I will show that closures of T-homogeneous braids form an infinite family of fibered links for which the corresponding open book can be braided.