Knots, Links, Braids And 3-manifolds: An Introduction To The New Invariants In Low-dimensional Topology (translations Of Mathematical Monographs)
by V. V. Prasolov /
1996 / English / DjVu
5.9 MB Download
This book is an introduction to the remarkable work of Vaughan
Jones and Victor Vassiliev on knot and link invariants and its
recent modifications and generalizations, including a mathematical
treatment of Jones-Witten invariants. It emphasizes the geometric
aspects of the theory and treats topics such as braids,
homeomorphisms of surfaces, surgery of 3-manifolds (Kirby
calculus), and branched coverings. This attractive geometric
material, interesting in itself yet not previously gathered in book
form, constitutes the basis of the last two chapters, where the
Jones-Witten invariants are constructed via the rigorous skein
algebra approach (mainly due to the Saint Petersburg school).
This book is an introduction to the remarkable work of Vaughan
Jones and Victor Vassiliev on knot and link invariants and its
recent modifications and generalizations, including a mathematical
treatment of Jones-Witten invariants. It emphasizes the geometric
aspects of the theory and treats topics such as braids,
homeomorphisms of surfaces, surgery of 3-manifolds (Kirby
calculus), and branched coverings. This attractive geometric
material, interesting in itself yet not previously gathered in book
form, constitutes the basis of the last two chapters, where the
Jones-Witten invariants are constructed via the rigorous skein
algebra approach (mainly due to the Saint Petersburg school).
Unlike several recent monographs, where all of these invariants
are introduced by using the sophisticated abstract algebra of
quantum groups and representation theory, the mathematical
prerequisites are minimal in this book. Numerous figures and
problems make it suitable as a course text and for self-study.
Unlike several recent monographs, where all of these invariants
are introduced by using the sophisticated abstract algebra of
quantum groups and representation theory, the mathematical
prerequisites are minimal in this book. Numerous figures and
problems make it suitable as a course text and for self-study.