Knots In Hellas '98 - Proceedings Of The International Conference On Knot Theory And Its Ramifications

Cameron Mca Gordon, Vaughan F R Jones, Louis H Kauffman

• Publisher: World Scientific
• Year: 2000
• Print ISBN:
  9789810243401
  9789810243401
• eBook ISBN:
  9789812792679
• Topic: Mathématiques
• Subtopic: Géométrie analytique

There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon-Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2,C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.

Table of contents

• Contents
• Preface
• TQFT INVARIANTS AT INFINITY FOR THE WHITEHEAD MANIFOLD
• GRIDS AS UNKNOTTING OPERATIONS
• On Simple Points Of Character Varieties Of 3-Manifolds
• THE 3-MOVE CONJECTURE FOR 5-BRAIDS
• A Faithful Representation of the Singular Braid Monoid on Three Strands
• New knot and link invariants
• GLUCK SURGERY AND FRAMED LINKS IN 4-MANIFOLDS
• The Planar Algebra of a bipartite graph
• CERTAIN RACKS ASSOCIATED WITH THE BRAID GROUPS
• AN EVALUATION OF THE COEFFICIENT POLYNOMIALS OF THE HOMFLY POLYNOMIAL OF A LINK
• ESTIMATING THE SIZE OF SKEIN HOMOLOGIES
• A Survey of Virtual Knot Theory
• LOWER BOUNDS FOR THE UNKNOTTING NUMBERS OF THE KNOTS OBTAINED FROM CERTAIN LINKS
• TORSION LINKING FORMS ON SURFACE-KNOTS AND EXACT 4-MANIFOLDS
• Extended Braids and Links
• On Spaces of connected Graphs I, Properties of Ladders
• Braid structures in knot complements, handlebodies and 3–manifolds
• On the remarkable properties of the hyperbolic Whitehead link cone-manifold
• MONTE CARLO EXPLORATIONS OF POLYGONAL KNOT SPACES
• MUTUAL BRAIDING AND THE BAND PRESENTATION OF BRAID GROUPS
• QUANTUM SU(2)-INVARIANTS FOR THREE-MANIFOLDS ASSOCIATED WITH NON-TRIVIAL COHOMOLOGY CLASSES MODULO TWO
• RELATIONS AMONG SELF DELTA-EQUIVALENCE AND SELF SHARP-EQUIVALENCES FOR LINKS
• Towards a complexity measure theory for vortex tangles
• PROJECTIONS OF CODIMENSION TWO EMBEDDINGS
• A KLEIN BOTTLE WHOSE SINGULAR SET CONSISTS OF THREE DISJOINT SIMPLE CLOSED CURVES
• SKEIN MODULES AND TQFT
• VIRTUAL KNOT GROUPS
• A ZETA-FUNCTION FOR A KNOT USING SL2(Fps) REPRESENTATIONS
• BRAID COMMUTATORS AND DELTA FINITE-TYPE INVARIANTS
• QUANTUM-LIKE PROPERTIES OF KNOTS AND LINKS
• Mutant links distinguished by degree 3 Gauß sums
• E6 TURAEV-VIRO-OCNEANU INVARIANT OF LENS SPACE L(p,1)
• Periodic knots with delta-unknotting number one
• THE KONTSEVICH INTEGRAL AND ALGEBRAIC STRUCTURES ON THE SPACE OF DIAGRAMS
• PROBLEMS
• ORGANISING COMMITTEE
• LIST OF PARTICIPANTS