Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Starting from knots and their colored Jones polynomials, we explain how surgery on framed links leads to Witten–Reshetikhin–Turaev invariants of 3-manifolds. For integral homology 3-spheres, Habiro assembles the invariants at roots of unity into a single element of the Habiro ring. We introduce this cyclotomic completion and its basic properties, explaining how evaluation at roots of unity and Taylor expansion connect quantum invariants with arithmetic.
Suggested references
Habiro, Cyclotomic completions of polynomial rings.
Habiro, A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres.
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