New Ideas In Low Dimensional Topology

New Ideas In Low Dimensional Topology

Louis H Kauffman, V O Manturov


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This book consists of a selection of articles devoted to new ideas and develpments 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.

  • Reidemeister / Roseman-Type Moves to Embedded Foams in 4-Dimensional Space (J Scott Carter)
  • How to Fold a Manifold (J Scott Carter and Seiichi Kamada)
  • Generalised Biquandles for Generalised Knot Theories (Roger Fenn)
  • Lectures on Knot Homology and Quantum Curves (Sergei Gukov and Ingmar Saberi)
  • Dirac Operators in Gauge Theory (Andriy Haydys)
  • Graph-Links: The State of the Art (D P Ilyutko, V O Manturov and I M Nikonov)
  • A Survey of Heegaard Floer Homology (András Juhász)
  • On the Framization of Knot Algebras (Jesús Juyumaya and Sofia Lambropoulou)
  • Virtual Knot Cobordism (Louis Hirsch Kauffman)
  • Mutant Knots (H R Morton)
  • Knots and Distributive Homology: From Arc Colorings to Yang–Baxter Homology (Józef H Przytycki)
  • Ordering Knot Groups (Dale Rolfsen)
  • Casson-Type Invariants from the Seiberg–Witten Equations (Daniel Ruberman and Nikolai Saveliev)

Readership: Researchers in knots theory and topology.