Triangulated surfaces in triangulated categories

The symmetries inherent in the structure constants of a Frobenius algebra can be used to associate certain numerical invariants of oriented surfaces. These numbers behave nicely when chopping surfaces into pieces - in technical terms they form a 2-dimensional open topological field theory. In particular, the invariant of a given surface can be computed in terms of a chosen triangulation. In this talk, we explain how certain symmetries in the foundations of homological algebra behave like a Frobenius algebra to the extent that they define invariants of oriented surfaces.

Based on joint work with Mikhail Kapranov.