The Mathematics of Knots

Theory and Application
2011
ISBN: 978-3-642-15636-6
Verlag: Springer

Buch, Englisch, 357 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 784 g

Reihe: Contributions in Mathematical and Computational Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Vogel, Denis

Banagl, Markus

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Preface.- 1 Knots, Singular Embeddings, and Monodromy.- 2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus.- 3 A Survey of Twisted Alexander Polynomials.- 4 On Two Categorifications of the Arrow Polynomial for Virtual Knots.- 5 An Adelic Extension of the Jones Polynomial.- 6 Legendrian Grid Number One Knots and Augmentations of their Differential Algebras.- 7 Embeddings of Four-Valent Framed Graphs into 2-Surfaces.- 8 Geometric Topology and Field Theory on 3-Manifolds.- 9 From Goeritz Matrices to Quasi-Alternating Links.- 10 An Overview of Property 2R.- 11 DNA, Knots and Tangles.