ISBN: 9780691036403

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. … More...

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. | Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134) Volume 134 by Louis H. Kauffman Paperback | Indigo Chapters Books > Science & Nature > Math & Physics > Mathematics > Geometry & Topology P10117, Louis H. Kauffman<

ISBN: 9780691036403

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. … More...

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. Books > Science & Nature > Math & Physics > Mathematics > Geometry & Topology List_Books, [PU: Princeton University Press]<

1994, ISBN: 9780691036403

Mitwirkende: Lins, Sostenes, Princeton University Press, Taschenbuch, 308 Seiten, Publiziert: 1994-07-25T00:00:01Z, Produktgruppe: Buch, 0.94 kg, Verkaufsrang: 5927, Geometrie, Naturwisse… More...

Mitwirkende: Lins, Sostenes, Princeton University Press, Taschenbuch, 308 Seiten, Publiziert: 1994-07-25T00:00:01Z, Produktgruppe: Buch, 0.94 kg, Verkaufsrang: 5927, Geometrie, Naturwissenschaft & Mathematik, Fachbücher, Kategorien, Bücher, Naturwissenschaften & Technik, Princeton University Press, 1994<

1994, ISBN: 9780691036403

Mitwirkende: Lins, Sostenes, Princeton University Press, Taschenbuch, 308 Seiten, Publiziert: 1994-07-25T00:00:01Z, Produktgruppe: Buch, 0.94 kg, Verkaufsrang: 5927, Geometrie, Naturwisse… More...

Mitwirkende: Lins, Sostenes, Princeton University Press, Taschenbuch, 308 Seiten, Publiziert: 1994-07-25T00:00:01Z, Produktgruppe: Buch, 0.94 kg, Verkaufsrang: 5927, Geometrie, Naturwissenschaft & Mathematik, Fachbücher, Kategorien, Bücher, Naturwissenschaften & Technik, Princeton University Press, 1994<