Gauss Diagram Invariants for Knots and Links

ISBN-13: 9789048157488 / Angielski / Miękka / 2010 / 412 str.

T. Fiedler

Opis

This book contains new numerical isotopy invariants for knots in the product of a surface (not necessarily orientable) with a line and for links in 3-space. These invariants, called Gauss diagram invariants, are defined in a combinatorial way using knot diagrams. The natural notion of global knots is introduced. Global knots generalize closed braids. If the surface is not the disc or the sphere then there are Gauss diagram invariants which distinguish knots that cannot be distinguished by quantum invariants. There are specific Gauss diagram invariants of finite type for global knots. These invariants, called T-invariants, separate global knots of some classes and it is conjectured that they separate all global knots. T-invariants cannot be obtained from the (generalized) Kontsevich integral. Audience: The book is designed for research workers in low-dimensional topology.

Spis treści

Preface. Introduction and announcement. 1. The space of diagrams. 2. Invariants of knots and links by Gauss sums. 3. Applications. 4. Global knot theory in F2xR. 5. Isotopies with restricted cusp crossing for fronts with exactly two cusps of Legendre knots in ST*R2. Bibliography. Index.