GAUSS Seminar

Matthew Barber
Understanding Ribbon Categories

In category theory and abstract algebra in general, it can sometimes be very difficult to knowwhen a composition of functions can be simplified. Then even if we know that thiscomposition does simplify, writing a proof for the equality might be a notational nightmarewhich results in a huge string of function compositions which can be extremely difficult tounderstand. Fortunately, there is a way to depict these function compositions using ribbonswhen the category you are working with has enough structure. These types of categories arecalled strict ribbon categories for this reason. When an isotopy exists between two ribbondiagrams, those two diagrams correspond to an equality of functions in the category.Therefore, we can use these ribbon diagrams to better understand long compositions offunctions and provide understandable proofs for why certain compositions can be simplified.In this talk we will establish the relationship between strict ribbon categories and ribbondiagrams by looking at the definition of a ribbon category and associating to eachrequirement a property of ribbon diagrams. This talk will follow the definition of a strict ribboncategory as defined by Turaev in his book, Quantum Invariants of Knots and 3-Manifold.

Event Date: 
November 1, 2023 - 4:30pm to 5:20pm
SH 3 or Online (See URL)
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