Knots, Low-Dimensional Topology and Applications

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. 

The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. 

The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. 

This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

• Knot Theory
• Virtual Knot Theory
• Low-Dimensional Topology
• Knot and Link Invariants
• Braids
• Skein Modules
• Topological Quantum Field Theory
• Quandles and their Homology
• Hyperbolic Knots
• Physical Knots
• Applications to Fluid Flows, to Polymers, to Natural Sciences
• DNA Enzyme Mechanisms
• Protein Structure and Function
• Biochemistry

• Department of Mathematics, Williams College, Williamstown, USA

  Colin C. Adams

• Department of Mathematics, University of Texas at Austin, Austin, USA

  Cameron McA. Gordon

• Department of Mathematics, Vanderbilt University, Nashville, USA

  Vaughan F.R. Jones

• Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, USA

  Louis H. Kauffman

• School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

  Sofia Lambropoulou

• Department of Mathematics, University of California, Santa Barbara, Santa Barbara, USA

  Kenneth C. Millett

• Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, USA

  Jozef H. Przytycki

• Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

  Renzo Ricca

• Department of Mathematics, North Carolina State University, Raleigh, USA

  Radmila Sazdanovic

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