Non-positive Stein-fillable open books of genus one
- Series
- Geometry Topology Seminar
- Time
- Monday, August 21, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Vitalijs Brejevs – University of Vienna – brejka@gmail.com
Contact 3-manifolds arise organically as boundaries of symplectic 4-manifolds, so it’s natural to ask: Given a contact 3-manifold Y, does there exist a symplectic 4-manifold X filling Y in a compatible way? Stein fillability is one such notion of compatibility that can be explored via open books: representations of a 3-manifold by means of a surface with boundary and its self-diffeomorphism, called a monodromy. I will discuss joint work with Andy Wand in which we exhibit first known Stein-fillable contact manifolds whose supporting open books of genus one have non-positive monodromies. This settles the question of correspondence between Stein fillings and positive monodromies for open books of all genera. Our methods rely on a combination of results of J. Conway, Lecuona and Lisca, and some observations about lantern relations in the mapping class group of the twice-punctured torus.