A Primer on Mapping Class Groups
by Benson Farb, Dan Margalit
Publisher: Princeton University Press 2011
Number of pages: 509
Our goal in this book is to explain as many important theorems, examples, and techniques as possible, as quickly and directly as possible, while at the same time giving (nearly) full details and keeping the text (nearly) selfcontained. This book contains some simplifications of known approaches and proofs, the exposition of some results that are not readily available, and some new material as well.
Download or read it online for free here:
by Louis H. Kauffman - University of Illinois at Chicago
This book is an introduction to knot theory and to Witten's approach to knot theory via his functional integral. Contents: Topics in combinatorial knot theory; State Models and State Summations; Vassiliev Invariants and Witten's Functional Integral.
by Eiji Ogasa - arXiv
This is an introductory article on high dimensional knots for the beginners. Is there a nontrivial high dimensional knot? We first answer this question. We explain local moves on high dimensional knots and the projections of high dimensional knots.
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 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.