Examples Class Schedule
1. Mon, 04/02/2019, 13:30 - 15:30, MR21.
1. Sphere and Torus Decompositions.
Allen Hatcher. Notes on Basic 3-Manifold Topology.
--Very hands-on. Uses logical but somewhat less conventional labels for Seifert data. We shall use β/α for a fiber of multiplicity α.
Danny Calegari. Notes on 3-Manifolds.
--Assumes a little more fluency in geometry, topology, and group theory, but approaches the subject from a broader perspective.
2a. The Alexander Polynomial.
Reagin Taylor McNeill. Knot Theory and the Alexander Polynomial.
-- An undergraduate thesis, but a very readable, well-organised reference on the
Alexander polynomial, with lots of explicit examples of calculations, especially in Fox calculus.
Daniel Copeland. The multivariable Alexander polynomial and Thurston norm.
-- The masters' thesis of a masters' student of András Stipsicz. Chapter 2 has a detailed exposition of the Alexander polynomial of a link exterior. A less explicit and somewhat more challenging read than McNeill's thesis, but shorter. Also discusses the Thurston norm.
2b. (Reidemeister-Milnor)-Turaev Torsion.
Liviu Nicolaescu. Notes on the Reidemeister Torsion.
-- I've had trouble finding a torsion reference which is both available online and reasonably gentle for an undergraduate audience. This reference at least satisfies the first condition. For a gentler reference not available online, see below.
Danny Calegari. Foliations and the geometry of 3-manifolds.
-- Chapters 4 and 5 will be the most relevant to our very brief treatment of foliations, and the book's introductory chapter has some useful discussion of mapping tori and the mapping class group, but this is also just a very fun book to explore.
Useful Offline References
J. Hempel, 3-Manifolds.
D. Rolfsen, Knots and Links.
R. Gompf and A. Stipsicz, 4-Manifolds and Kirby Calculus.
V. Turaev, Introduction to Combinatorial Torsions.
Danny Calegari, Foliations and the geometry of 3-manifolds.
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