FUNCTORIAL KNOT THEORY (eBook)

Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants

David N Yetter (Autor)

eBook Download: PDF

2001
236 Seiten
World Scientific Publishing Company (Verlag)
978-981-281-046-5 (ISBN)

Infos

Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.

Produkt-Details

• Erscheint lt. Verlag: 16.4.2001
• Reihe/Serie: Series On Knots And Everything
• Reihe/Serie: Series On Knots And Everything
• Reihe/Serie: SERIES ON KNOTS AND EVERYTHING
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 981-281-046-3 / 9812810463
• ISBN-13: 978-981-281-046-5 / 9789812810465