CDBooK: Introduction to Vassiliev Knot invariants
by S.Chmutov, S.Duzhin, J.Mostovoy
Publisher: Ohio State Universit 2009
Number of pages: 460
This text provides an introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended for readers with no or little background in this area, and we care more about a clear explanation of the basic notions and constructions than about widening the exposition to more recent and more advanced material.
Home page url
Download or read it online for free here:
by A. A. Ranicki - Cambridge University Press
Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds.
by M. Boittin, E. Callahan, D. Goldberg, J. Remes - Ohio State University
This is an innovative project by a group of Yale undergraduates: A Multi-Disciplinary Exploration of Non-Orientable Surfaces. The course is designed to be included as a short segment in a late middle school or early high school math course.
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
by Jonathan Hillman - arXiv
The goal of the book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such knots.