Venue
Aula Seminari - Dipartimento di Matematica
Abstract
The theory of braid foliations was developed to study knots and links, as well as surfaces in 3-manifolds. The original idea goes back to Bennequin and his works on exotic contact structures on $\mathbb{R}^3$ (1989) and was then developed by Birman and Menasco in a series of papers during the 90’s. These techniques have proved to be very useful to solve many foundational problems in braid theory and contact topology, such as Jones conjecture, the Legendrian grid number conjecture, Bennequin’s inequality, transverse Markov theorem and many others. In this talk we will see a proof by means of braids foliations of Markov theorem, a fundamental result connecting braids and links. This proof is due
to Birman and Menasco (2002).