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.
Home page url
Download or read it online for free here:
by Dennis Sullivan - Springer
In 1970, Sullivan circulated this set of notes introducing localization and completion of topological spaces to homotopy theory, and other important concepts. The notes remain worth reading for the fresh picture they provide for geometric topology.
by Danny Calegari - Oxford University Press
The book gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
by F.T. Farrell - Springer
This book is an introduction to the topological rigidity theorem for compact non-positively curved Riemannian manifolds. It contains a quick informal account of the background material from surgery theory and controlled topology prerequesite.
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.