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Springer Gauss Diagram Invariants for Knots and Links - Mathematics & Applications 532

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Description

Gauss Diagram Invariants for Knots and Links by Springer explores isotopy invariants of oriented knots in manifolds that are products of surfaces with oriented lines. This mathematics text defines invariants combinatorially using knot diagrams, with values in free abelian groups generated by surface homology or free homotopy classes. The work presents three main results including construction of finite type invariants for arbitrary knots in non-orientable 3-manifolds, invariants that distinguish homotopic knots with homeomorphic complements, and applications to knot theory. Part of the Mathematics and Its Applications series (volume 532), this book provides rigorous mathematical treatment for researchers and advanced students studying knot invariants, topology, and geometric analysis of knot structures.

Key Features

Gauss diagram invariants provide isotopy invariants for oriented knots in product manifolds of surfaces with oriented lines.

Combinatorial definitions use knot diagrams with values in free abelian groups generated by surface homology or homotopy classes.

Construction of finite type invariants for arbitrary knots in non-orientable 3-manifolds enables classification of complex knot structures.

Invariants distinguish homotopic knots with homeomorphic complements, offering powerful differentiation tools for knot theory research.

Volume 532 in Springer's Mathematics and Its Applications series provides academic rigour for graduate-level topology study.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
15 December 2010
Listed Since
20 September 2010

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