Georgios Dimitroglou Rizell (Uppsala University) will speak in the geometry seminar on the 13th of March. The talk will take place in the Salle de Profs (9th floor, NO) at 13.30pm. Georgios’ title is “Bulk-deformed augmentations do not correspond to sheaves” and the abstract is below.
We exhibit nullhomologous Legendrian spheres in one-jet spaces whose Chekanov-Eliashberg algebras admit augmentations only after “bulk deformation” or, equivalently, using Novikov coefficients in the group ring of relative homology. (In fact the dg-algebra is acyclic when normal coefficents are used.) These Legendrians are also studied from the point-of-view of a different powerful Legendrian isotopy invariant: constructible sheaves; we argue why there are no sheaves with microsupport equal to these Legendrians. The conclusion is that bulk-deformation is not captured by the standard category of sheaves. This is work in progress together with H. Gao and Y. Huang.