Functorial گره تئوری: دسته بندی ها از دولایه ، انسجام، طبقه تغییر شکل و ویژگیهای topological Functorial Knot Theory : Categories of Tangles, Coherence, Categorical Deformations and Topological Invariants
- نوع فایل : کتاب
- زبان : انگلیسی
- نویسنده : David N. Yetter
- ناشر : World Scientific Publishing Company
- چاپ و سال / کشور: 2001
- شابک / ISBN : 9810244436, 9789810244439
Description
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 structure 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.
