Date of Award:
Master of Science (MS)
Mathematics and Statistics
Invariants of knots and links are useful because they give rise to invariants of 3-manifolds. In particular, combinatorial link invariants give rise to combinatorial invariants of 3-manifolds, which are hard to come by using traditional methods from classical topology. The Reshetikhin–Turaev approach, which is based in quantum topology, develops link invariants using semisimple ribbon categories. However, a large class of algebraically interesting ribbon categories are non-semisimple and so give trivial link invariants via the Reshetikhin–Turaev method. We modify the Reshetikhin–Turaev method to make it suitable for non-semisimple ribbon categories. We discuss explicitly the following three examples: semisimple modules for the abelian quantum group, non-semisimple modules for Uq(gl(1|1)), and non-semisimple modules for the unrolled quantum group of sl2(C).
Robertson, Adam, "Using the Reshetikhin-Turaev Link Invariant Approach with Non-Semisimple Categories" (2022). All Graduate Theses and Dissertations. 8586.
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .