Miguel Orbegozo Rodríguez: "Monodromies of surfaces in 3-manifolds"

mardi 31 mars 2026, 15:00 → 16:00 Europe/Paris

Salle 318 (IMB)

A surface $S$ (compact, connected, oriented, usually with boundary) in a 3-manifold is a fiber surface if the 3-manifold can be obtained by taking $S \times [0,1]$ and gluing the two ends by a diffeomorphism $h$, called the monodromy. The pair $(S,h)$ carries information about both the link on the boundary of $S$ (for example, whether it decomposes as a connected sum), and the 3-manifold itself (for example, following Thurston, whether it is Seifert fibered, toroidal, or hyperbolic).  However, these techniques are in some way restrictive because if S is not a fiber surface, they do not apply (for example, they do not even apply to all knot complements in $S^3$). In this talk I will present a version of monodromy which is defined for all incompressible surfaces in 3-manifolds, and not just fiber ones. It takes the form of a partially defined map on isotopy classes of arcs and curves instead of a diffeomorphism. I will then show that with this new notion of monodromy, most properties that can be extracted from fiber surfaces can also be obtained from general incompressible surfaces. This is joint work with Peter Feller and Lukas Lewark, and parts of the talk will feature joint work in progress with Peter Feller.