On the topological characterization of gestures in a convenient category of spaces

Abstract

ABSTRACT In this paper, we reconsider the topological characterization of gestures in a convenient category of spaces mentioned by Mazzola in 2009, recovering Arias's 2018 result that the relevant equivalence is a homeomorphism. We also show the topological characterization of gestures extends to an adjunction between the category of gestures and the category of continuous maps whose domain is a one-dimensional CW complex. Our arguments utilize only basic tools from category theory and almost no point-set topology. With little generality lost from our restriction of spaces considered, the ease of conceptualization in this setting provides an advantageous entry point for researchers interested in studying or applying gestures but who may not have advanced knowledge of category theory, algebraic geometry, or point-set topology. Thus one may view this work, in part, as an advertisement for the topological interpretation of gestures developed within.