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El. knyga: Mathematics of Knots: Theory and Application

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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.

This book offers up-to-date original research and survey articles on actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. The contents arise from the Heidelberg Knot Theory Semester of winter 2008-09.
1 Knots, Singular Embeddings, and Monodromy
1(30)
Markus Banagl
Sylvain E. Cappell
Julius L. Shaneson
2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus
31(14)
Kumud Bhandari
H.A. Dye
Louis H. Kauffman
3 A Survey of Twisted Alexander Polynomials
45(50)
Stefan Fried]
Stefano Vidussi
4 On Two Categorifications of the Arrow Polynomial for Virtual Knots
95(30)
Heather Ann Dye
Louis Hirsch Kauffman
Vassily Olegovich Manturov
5 An Adelic Extension of the Jones Polynomial
125(18)
Jesus Juyumaya
Sofia Lambropoulou
6 Legendrian Grid Number One Knots and Augmentations of Their Differential Algebras
143(26)
Joan E. Licata
7 Embeddings of Four-valent Framed Graphs into 2-surfaces
169(30)
Vassily Olegovich Manturov
8 Geometric Topology and Field Theory on 3-Manifolds
199(58)
Kishore Marathe
9 From Goeritz Matrices to Quasi-alternating Links
257(60)
Jozef H. Przytycki
10 An Overview of Property 2R
317(10)
Martin Scharlemann
11 DNA, Knots and Tangles
327(28)
De Witt Sumners
Workshop Talks 355