Algebraic L-theory and Topological Manifolds
by A. A. Ranicki
Publisher: Cambridge University Press 2011
Number of pages: 365
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, in a unified algebraic framework.
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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.
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 Liviu I. Nicolaescu - World Scientific Publishing Company
An introduction to the most frequently used techniques in modern global geometry. Suited to the beginning graduate student, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.
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.