The mathematics of knots theory and application ; [grew out of the Heidelberg knot theory semester ... in winter 2008 09 at Heidelberg University

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands. Front Matter....Pages I-X Knots, Singular Embeddings, and Monodromy....Pages 1-30 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus....Pages 31-43 A Survey of Twisted Alexander Polynomials....Pages 45-94 On Two Categorifications of the Arrow Polynomial for Virtual Knots....Pages 95-124 An Adelic Extension of the Jones Polynomial....Pages 125-142 Legendrian Grid Number One Knots and Augmentations of Their Differential Algebras....Pages 143-168 Embeddings of Four-valent Framed Graphs into 2-surfaces....Pages 169-197 Geometric Topology and Field Theory on 3-Manifolds....Pages 199-256 From Goeritz Matrices to Quasi-alternating Links....Pages 257-316 An Overview of Property 2R....Pages 317-325 DNA, Knots and Tangles....Pages 327-353 Back Matter....Pages 355-357