Date of Award:
8-2022
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Matthew Young
Committee
Matthew Young
Committee
Nghiem Nguyen
Committee
Nathan Geer
Abstract
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).
Checksum
d7f3c2c7b2751532d02fecf9263f3957
Recommended Citation
Robertson, Adam, "Using the Reshetikhin-Turaev Link Invariant Approach with Non-Semisimple Categories" (2022). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 8586.
https://digitalcommons.usu.edu/etd/8586
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