Download Winding Numbers and Monodromy of Vector Bundles over a Circular Buffer The Möbius strip is perhaps the most recognizable topological object of general knowledge. It can be described mathematically in various ways including the formalism of line bundles. In this paper we discuss the bundle idea in the context of digital processing over a circular buffer and show how the idea leads to a more general notion known as monodromy, which describes the effect of the space on traversing a circle once. In this formulation, the monodromy of the Möbius strip is an orientation inversion characterized by a change in sign. This in turns leads to the concept of the winding number, which describes how many windings it takes to return to the original state. We discuss variable monodromy and illustrate that the winding number is robust under this variation. This will allow us to interpret previous disparate results in audio signal processing from Möbius waveguides to chaotic oscillators in delay loops in one unified framework. We close by showing how extending from line to vector bundles opens up the notion of braids to describe monodromy.