A Topology Primer
by Klaus Wirthmüller
Publisher: Technische Universität Kaiserslautern 2002
Number of pages: 197
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 successfully completed their first year courses in analysis and linear algebra.
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by Jean-Pierre Schneiders - Universidade de Lisboa
This text deals with characteristic classes of real and complex vector bundles and Hirzebruch-Riemann-Roch formula. We will present a few basic but fundamental facts which should help the reader to gain a good idea of the mathematics involved.
by R. R. Bruner, J. P. May, J. E. McClure, M. Steinberger - Springer
This volume concerns spectra with enriched multiplicative structure. It is a truism that interesting cohomology theories are represented by ring spectra, the product on the spectrum giving rise to the cup products in the theory.
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Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
by Andrew Ranicki - Oxford University Press
Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.