Description
Book SynopsisThis book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.
Table of ContentsCasson-Type Invariants from the Seiberg-Witten Equations (D Ruberman and N Saveliev); Dirac Operators in Gauge Theory (A Haydys); How to Fold a Manifold (J Scott Carter and S Kamada); Generalised Biquandles for Generalised Knot Theories (R Fenn); Graph-Links: The State of the Art (D P Ilyutko, V O Manturov, I M Nikonov); Lectures on Knot Homology and Quantum Curves (S Gukov and I Saberi); Reidemeister / Roseman-type Moves to Embedded Foams in 4-dimensional Space (J Scott Carter); Virtual Knot Cobordism (L H Kauffman); Mutant Knots (H R Morton); Ordering Knot Groups (D Rolfsen); A Survey of Heegaard Floer Homology (A Juhasz); On the Framization of Knot Algebras (J Juyumaya & S Lambropoulou) and other papers;
