Columbia Mathematics Department Colloquium


Triangulated surfaces
in triangulated categories


Mikhail Kapranov




Standard axioms of triangulated categories
(passing from one diagram of exact triangles to another)
can be interpreted in terms of flips of 2-dimensional triangulations.
This allows us to consider diagrams of exact triangles
corresponding to triangulated surfaces. In particular,
one can construct the "universal" triangulated category
containing such a diagram corresponding to a given
triangulation of a surface. This category is a topological
invariant of the surface (together with the fixed set
of marked points serving as vertices) and can be
considered as a combinatorial version of the Fukaya
category. This talk is based on a joint work with T. Dyckerhoff.


Wednesday, Nov. 20, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.