An Introduction to Algebraic Surgery
by Andrew Ranicki
Publisher: arXiv 2000
Number of pages: 82
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 (such as the Wall surgery obstruction groups), without losing sight of the geometric motivation.
Home page url
Download or read it online for free here:
by Liviu I. Nicolaescu - University of Notre Dame
The author discusses several exciting topological developments which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.
by D. G. Bourgin - Macmillan
Contents: Preliminary algebraic background; Chain relationships; The absolute homology groups and basic examples; Relative omology modules; Manifolds and fixed cells; Omology exact sequences; Simplicial methods and inverse and direct limits; etc.
by Klaus Wirthmüller - Technische Universität Kaiserslautern
The purpose of this text is to make familiar with the basics of topology, to give a concise introduction to homotopy, and to make students familiar with homology. Readers are expected to have knowledge of analysis and linear algebra.
by Dikran Dikranjan - UCM
These notes provide a brief introduction to topological groups with a special emphasis on Pontryaginvan Kampen's duality theorem for locally compact abelian groups. We give a completely self-contained elementary proof of the theorem.