## Columbia Mathematics Department Colloquium

Triangulated surfaces

in triangulated categories

in triangulated categories

by

# Mikhail Kapranov

# (Yale)

Abstract:

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.

(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.