Surgical Methods in Rigidity
by F.T. Farrell
Publisher: Springer 1996
Number of pages: 108
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 to this result. It is intended for researchers and advanced graduate students in both differential geometry and topology.
Download or read it online for free here:
by J. P. May - Springer
The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.
by S.Chmutov, S.Duzhin, J.Mostovoy - Ohio State Universit
An introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. Written for readers with no background in this area, and we care more about the basic notions than about more advanced material.
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 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.