Gauss Diagram Invariants for Knots and Links
By: by Thomas Fiedler
Series: Mathematics and Its Applications -- 532; Mathematics and Its Applications -- 532
Publisher: Springer Netherlands
Published: 2001
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 428
ISBN-13: 9789048157488; 9789401597852
Subjects: Geometry; Mathematics; Cell aggregation
Description: 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.
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