Melvin Vaupel, Extending Dowkers duality theorem and a possible application to neural data analysis.

I will motivate and construct an extension of the filtered Dowker complex of a relation. I will argue how this bi-filtered complex provides a much more complete summary of the homotopical content of the underlying relation. As for the ordinary Dowker complex one may consider a dual complex associated to the relations transpose. I state and proof an appropriate functorial duality theorem which extends Dowkers original theorem. Finally I explain how the extended Dowker complex may solve issues in the topological analysis of neural datasets as was already hinted to in my previous talk.