High-dimensional Knot Theory
by Andrew Ranicki
Publisher: Springer 1998
Number of pages: 693
This book is devoted entirely to high-dimensional knot theory. It actually has two aims: (1) to serve as an introduction to high-dimensional knot theory, using surgery theory to provide a systematic exposition, (2) to serve as an introduction to algebraic surgery theory, using high-dimensional knots as the geometric motivation.
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by Andrew Ranicki - arXiv
Browder-Novikov-Sullivan-Wall surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory.
by David Bachman - arXiv
This is a textbook on differential forms. The primary target audience is sophomore level undergraduates enrolled in a course in vector calculus. Later chapters will be of interest to advanced undergraduate and beginning graduate students.
by William P Thurston - Mathematical Sciences Research Institute
The text describes the connection between geometry and lowdimensional topology, it is useful to graduate students and mathematicians working in related fields, particularly 3-manifolds and Kleinian groups. Much of the material or technique is new.
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.