Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 (eBook)

Louis H. Kauffman, Sostenes Lins (Autoren)

eBook Download: PDF

2016
312 Seiten
Princeton University Press (Verlag)
978-1-4008-8253-3 (ISBN)

Infos

Louis H. Kauffman is Professor of Mathematics at the University of Illinois, Chicago. Sostenes Lins is Professor of Mathematics at the Universidade Federal de Pernambuco in Recife, Brazil.

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This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 1200 illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: 3-manifold • Addition • algorithm • Ambient isotopy • Axiom • Backslash • Barycentric subdivision • bijection • bipartite graph • Borromean Rings • Boundary parallel • bracket polynomial • Calculation • canonical form • Cartesian Product • Cobordism • coefficient • combination • commutator • Complex conjugate • Computation • Connected component (graph theory) • Connected sum • Cubic graph • Diagram (category theory) • Dimension • Disjoint sets • Disjoint union • Elaboration • Embedding • Equation • equivalence class • Explicit formula • Explicit formulae (L-function) • factorial • fundamental group • Graph (discrete mathematics) • graph embedding • Handlebody • Homeomorphism • Homology (mathematics) • Identity element • Intersection form (4-manifold) • Inverse function • Jones polynomial • Kirby calculus • knot theory • Linear Independence • Line segment • Matching (graph theory) • Mathematical Physics • Mathematical Proof • Mathematics • Maxima and minima • Monograph • Natural number • Network Theory • Notation • Numerical analysis • Orientability • orthogonality • Pairing • pairwise • parametrization • Parity (mathematics) • Partition function (mathematics) • Permutation • Poincaré conjecture • polyhedron • Quantum group • quantum invariant • Recoupling • Recursion • Reidemeister move • result • Roger Penrose • Root of unity • scientific notation • Sequence • Significant figures • Simultaneous Equations • smoothing • Special case • Sphere • Spin Network • Summation • Symmetric group • tetrahedron • The Geometry Center • Theorem • theory • Three-dimensional space (mathematics) • time complexity • Tubular neighborhood • two-dimensional space • Vector field • Vector Space • Vertex (graph theory) • Winding number • Writhe
• ISBN-10: 1-4008-8253-2 / 1400882532
• ISBN-13: 978-1-4008-8253-3 / 9781400882533