On Open and Closed Strings

Abstract

Cobordism categories are highly complicated structures that can be analyzed by way of their classifying spaces. In the case of surfaces, meaning $2$-dimensional cobordisms, this has led to many important results in recent years. This paper studies the subcategory of open strings of the category of open and closed strings as introduced by Baas, Cohen and Ramírez and identifies the homotopy type of its classifying spaces.