# Categorification of Reeb Graphs

Tuesday, October 22, 2013 - 1:30pm - 2:30pm

Lind 305

Elizabeth Munch (University of Minnesota, Twin Cities)

In order to understand the properties of a real-valued function on a

topological space, we can study the Reeb graph of that function. Since it

is efficient to compute and is a useful descriptor for the function, it has

found its place in many applications. As with many other constructions in

computational topology, we are interested in how to deal with this

construction in the context of noise. In particular, we would like a

method to smooth out the topology to get rid of, for example, small loops

in the Reeb graph.

In this talk, we will define a generalization of a Reeb graph as a

functor. Using the added structure given by category theory, we can define

interleavings on Reeb graphs. This also gives an immediate method for

topological smoothing and we will discuss an algorithm for computing this

smoothed Reeb graph.

topological space, we can study the Reeb graph of that function. Since it

is efficient to compute and is a useful descriptor for the function, it has

found its place in many applications. As with many other constructions in

computational topology, we are interested in how to deal with this

construction in the context of noise. In particular, we would like a

method to smooth out the topology to get rid of, for example, small loops

in the Reeb graph.

In this talk, we will define a generalization of a Reeb graph as a

functor. Using the added structure given by category theory, we can define

interleavings on Reeb graphs. This also gives an immediate method for

topological smoothing and we will discuss an algorithm for computing this

smoothed Reeb graph.