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The mathematics of knots theory and application 1st Edition by Markus Banagl, ‎Denis Vogel ISBN 9783642156373

  • SKU: BELL-20009746
The mathematics of knots theory and application 1st Edition by Markus Banagl, ‎Denis Vogel ISBN 9783642156373
$ 31.00 $ 45.00 (-31%)

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The mathematics of knots theory and application 1st Edition by Markus Banagl, ‎Denis Vogel ISBN 9783642156373 instant download after payment.

Publisher: Springer
File Extension: PDF
File size: 4.62 MB
Author: Banagl, Markus(Editor);Vogel, Denis(Editor)
ISBN: 9783642156366, 9783642156373, 3642156363, 3642156371
Language: English
Year: 2010

Product desciption

The mathematics of knots theory and application 1st Edition by Markus Banagl, ‎Denis Vogel ISBN 9783642156373 by Banagl, Markus(editor);vogel, Denis(editor) 9783642156366, 9783642156373, 3642156363, 3642156371 instant download after payment.

The mathematics of knots theory and application 1st Edition by Markus Banagl, ‎Denis Vogel - Ebook PDF Instant Download/Delivery: 9783642156373
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ISBN 13: 9783642156373
Author: Markus Banagl, ‎Denis Vogel

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.

The mathematics of knots theory and application 1st Table of contents:

  1. Introduction
  2. Organization
  3. Blanchfield and Poincaré Local Systems
  4. Passage from Blanchfield Systems to Poincaré Systems
  5. Passage from Poincaré Systems to Complex Hermitian Systems
  6. Strongly Transverse Poincaré Local Systems
  7. Computing Twisted L-Classes for Strongly Transverse Coefficients
  8. The Cappell-Shaneson L-Class Formula for Singular Embeddings
  9. Embeddings and Strongly Transverse Coefficients
  10. Nontransverse Coefficient Systems
  11. References
  12. Lower Bounds on Virtual Crossing Number and Minimal Surface Genus
  13. The Arrow Polynomial
  14. Computations
  15. Knot 4.01
  16. Knot 4.09
  17. Knot 4.22
  18. Knot 4.47
  19. Knot 4.91
  20. Knot 4.99
  21. Knots with Arrow Polynomial One
  22. References
  23. A Survey of Twisted Alexander Polynomials
  24. Introduction
  25. Conventions and Notation
  26. Definition and Basic Properties
  27. Twisted Reidemeister Torsion
  28. Computation of Twisted Reidemeister Torsion
  29. Torsion Invariants
  30. Twisted Alexander Invariants
  31. Computation of Twisted Alexander Polynomials
  32. Basic Properties of Twisted Invariants
  33. Relationship Between Twisted Invariants
  34. Twisted Invariants for Conjugate Representations
  35. Change of Variables
  36. Duality for Twisted Invariants
  37. Shapiro's Lemma for Twisted Invariants
  38. Twisted Invariants of Knots and Links
  39. Distinguishing Knots and Links
  40. Twisted Alexander Polynomials and Concordance
  41. Twisted Alexander Polynomials of Zero-Surgeries
  42. Twisted Alexander Polynomials and Knot Concordance
  43. Ribbon Knots and Doubly Slice Knots
  44. Twisted Invariants and Slice Links
  45. Twisted Alexander Polynomials, the Thurston Norm and Fibered Manifolds
  46. Twisted Alexander Polynomials and Fibered Manifolds
  47. Twisted Alexander Polynomials and the Thurston Norm
  48. Normalized Twisted Reidemeister Torsion and the Free Genus of a Knot
  49. Twisted Invariants of Knots and Special Representations
  50. Parabolic Representations
  51. Twisted Alexander Polynomials and the Space of 2-Dimensional Representations
  52. Twisted Invariants of Hyperbolic Knots and Links
  53. Metabelian Representations
  54. Miscellaneous Applications of Twisted Reidemeister Torsion to Knot Theory
  55. A Partial Order on Knots
  56. Periodic and Freely Periodic Knots
  57. Zeroes of Twisted Alexander Polynomials and Non-abelian Representations
  58. Seifert Fibered Surgeries
  59. Homology of Cyclic Covers
  60. Alexander Polynomials for Links in R P3
  61. Twisted Alexander Polynomials of CW-complexes and Groups
  62. Definitions and Basic Properties
  63. Twisted Alexander Polynomials of Groups
  64. Plane Algebraic Curves
  65. Alexander Polynomials and Representations over Non-commutative Rings
  66. Non-commutative Alexander Polynomials
  67. Higher Order Alexander Polynomials
  68. Comparing Different phi-Compatible Maps
  69. Miscellaneous Applications of Higher Order Alexander Polynomials
  70. Open Questions and Problems
  71. References
  72. On Two Categorifications of the Arrow Polynomial for Virtual Knots
  73. Introduction
  74. The Arrow Polynomial A
  75. Khovanov Homology for Virtual Knots
  76. Grading Considerations for the Arrow Polynomial A
  77. Dotted Gradings and the Dotted Categorification
  78. Z2-Categorification with General Gradings
  79. General Setup
  80. Part 1. Proof that the Complex is Well Defined
  81. Notation
  82. Part 2. Proof that the Homology is Invariant Under Reidemeister Moves
  83. Explanation for the Second and the Third Moves
  84. Applications
  85. Open Questions
  86. References
  87. An Adelic Extension of the Jones Polynomial
  88. Introduction
  89. An Adelic Representation of the Braid Group
  90. The Yokonuma-Hecke Algebra
  91. The Adelic Yokonuma-Hecke Algebra
  92. Representing the Braid Group
  93. An Adelic Markov Trace
  94. The Modular Markov Trace trd
  95. The Adelic Markov Trace trinfty
  96. The E-Condition
  97. Why E-Condition
  98. The E-System
  99. Lifting Solutions of the E-System
  100. An Adelic Extension of the Jones Polynomial
  101. Isotopy Invariants from trd
  102. Computations
  103. A Cubic Skein Relation for Deltad, S
  104. An Isotopy Invariant from trinfty
  105. References
  106. Legendrian Grid Number One Knots and Augmentations of Their Differential Algebras
  107. Introduction
  108. Main Results
  109. Conventions and Organization
  110. Background
  111. Contact Lens Spaces
  112. Grid Diagrams
  113. Differential Graded Algebras
  114. The Lagrangian DGA for KL(p,q)
  115. The Defect
  116. The Boundary Map
  117. Converting Fronts to Lagrangian Projections
  118. Special Front Projections
  119. The Lagrangian Projection Associated to a Special Front
  120. Augmentations of (A(K0), )
  121. The Grading
  122. Special Boundary Discs
  123. Boundary Maps of a-Type Generators
  124. Applications
  125. Augmentations for (A(K(p,p-1,1)), )
  126. Augmentations of (A(K(p,p-1,2)),)
  127. References
  128. Embeddings of Four-valent Framed Graphs into 2-surfaces
  129. Introduction
  130. Atoms and Knots
  131. Notation
  132. Chord Diagrams, 1-dimensional Surgery and the Kauffman Bracket
  133. The Source-sink Condition
  134. The Planar Case: Vassiliev's Conjecture
  135. The Case of RP2
  136. The Case of the Klein Bottle
  137. The Chord Diagram Algebra and the Graph Algebra
  138. The Generating Function for the Embedding Genera
  139. Weight Systems Associated with Lie Algebras: a Brief Review
  140. Checkerboard Colourable Embeddings
  141. Embeddings with Orienting Z2-homology Class
  142. The General Case
  143. Unsolved Problems
  144. References
  145. Geometric Topology and Field Theory on 3-Manifolds
  146. Introduction
  147. Gauss' Formula for Linking Number of Knots
  148. Supersymmetry and Morse Theory
  149. Graded Algebraic Structures
  150. Monstrous Moonshine
  151. SUSY Quantum Theory
  152. Chern-Simons Theory
  153. Flat Connections
  154. Casson Invariant and Flat Connections
  155. Fukaya-Floer Homology
  156. Knot Polynomials
  157. Categorification of Knot Polynomials
  158. Categorification of V(31)
  159. Topological Quantum Field Theory
  160. Atiyah-Segal Axioms for TQFT
  161. Quantum Observables
  162. Wilson Loop Functional
  163. Link Invariants
  164. WRT Invariants
  165. CFT Approach to WRT Invariants
  166. WRT Invariants via Quantum Groups
  167. Chern-Simons and String Theory
  168. Conifold Transition
  169. WRT Invariants and String Amplitudes
  170. Yang-Mills, Gravity and Strings
  171. Gravitational Field Equations
  172. Geometrization Conjecture and Gravity
  173. References
  174. From Goeritz Matrices to Quasi-alternating Links
  175. Short Historical Introduction
  176. Precision Comes to Knot Theory
  177. Lattice Knots of Dehn and Heegaard
  178. Early Invariants of Links
  179. Kirchhoff's Complexity of a Graph
  180. Tait's Relation Between Knots and Graphs
  181. Link Diagrams and Reidemeister Moves
  182. Goeritz Matrix and Signature of a Link
  183. Seifert Surfaces
  184. Connected Sum of Links
  185. Linking Number; Seifert Forms and Matrices
  186. From Seifert form to Alexander Polynomial and Signatures
  187. Tristram-Levine Signature
  188. Potential Function and Tristram-Levine Signature
  189. A Combinatorial Formula for the Signature of Alternating Diagrams; Quasi-alternating Links
  190. Quasi-alternating Links
  191. References
  192. An Overview of Property 2R
  193. Generalizing Property R
  194. Property 2R
  195. The 4-manifold Viewpoint: A Non-standard Handle Structure on S4
  196. References
  197. DNA, Knots and Tangles
  198. Introduction
  199. Topological Enzymology
  200. Site-Specific Recombination
  201. Knots and Tangles
  202. The Tangle Model for Site-Specific Recombination
  203. The Topology of Tn3 Resolvase
  204. References
  205. Workshop Talks

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Tags: Markus Banagl, ‎Denis Vogel, mathematics, knots

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