Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Recapitulation of basic manifold theory, fundamental groups and covering spaces.
- Knots and links, equivalence of knots, isotopy of knots, knot diagrams, Reidemeister moves.
- Basic operations of knots, mirror image, connected sum, Whitehead double, torus links.
- Basic link invariants, unknotting number, linking number, knot groups and their Wirtinger presentations, 3-colorings of knots, Seifert surfaces and knot genus, Jones and Alexander polynomials of knots.
- Braids, braid groups, knots as closures of braids, Alexander's theorem, Markov's Theorem, representations of braid groups, automorphisms of braid groups, generalisations of braid groups.
- Quandles, construction of knot quandle, quandle cohomology, construction of knot invariants using quandles.
- Joan S. Birman, Braids, Links, and Mapping Class Groups,. (AM-82), Annals of Mathematics Studies, 1974.
- R. H. Crowell and R. H. Fox, Introduction to Knot Theory, Springer Verlag, 1963.
- M. Elhamdadi and S. Nelson, Quandles: An Introduction to the Algebra of Knots, American Mathematical Society, 2015.
- C. Kassel and V. Turaev, Braid Groups, Springer Verlag, 2008.
- A. Kawauchi, A Survey of Knot Theory, Birkhäuser Basel, 1996.
