An informal learning seminar on the analogy between number fields and 3-manifolds, organized by Autumn Kent and Melanie Matchett Wood
Tuesdays, 11:15am-Noon Van Vleck B203
April 2: Autumn and Melanie describe the basic objects, some of the big questions about them, on both sides of the analogy, e.g. see Section 2.2 of Analogies between group actions on 3-manifolds and number fields by Sikora or Section 14 of Hakenness and b_1 by Reznikov.
April 9: Basic objects, continued
April 16: Splitting, inertia groups, and ramification
April 23: Quadratic Reciprocity
April 30: no meeting
May 7: Chebotarev density theorem
Knots and Primes, book by Morishita (Melanie has from library, you can borrow)
A list of some other references
Quadratic reciprocity and symmetry of the linking number (see Li-Sia notes above).
Genus theory and topological analog (classification of the homology classes of the homology group by linking numbers?) (Ch 6 of Knots and Primes book)
Structure of link groups and Galois groups with restricted ramification Paper by Morishita
Alexander Polynomial and Iwasawa Theory (Ch 9 of Knots and Primes book)
Class field theory and analog for knots Paper by Niibo
``Knots which behave like the prime numbers'' by McMullen on Chebotarev density theorem for 3-manifolds.