## Geometry and Topology

•  Stéphane Guillermou, Institut Fourier
•  Stable Gauss map of nearby Lagrangians
•  11/24/2020
•  11:00 AM - 11:59 AM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Honghao Gao (gaohongh@msu.edu)

The stable Gauss map of a Lagrangian $L$ in a cotangent $T^*M$ is a map $g \colon L \to U/O$ obtained by stabilization of the usual Gauss map from $L$ to the Lagrangian Grassmannian of $T^*M$. Arnold's conjecture on nearby Lagrangians implies in particular that $g$ is homotopic to a constant map. We will see the weaker result that the map induced by $g$ on the homotopy groups is trivial. By a theorem of Giroux and Latour $g$ is homotopic to a constant map if and only if $L$ admits a generating function. We introduce twisted'' generating functions as a tool to the study of $L$ and make the link with difficult results of pseudo-isotopy theory. This is a joint work with Mohammed Abouzaid, Sylvain Courte and Thomas Kragh. https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09

## Contact

Department of Mathematics
Michigan State University