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 Daniel Dugger - University of Oregon
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.
by Boris Dubrovin - arXiv
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Topics: WDVV equations and Frobenius manifolds; Polynomial solutions of WDVV; Symmetries of WDVV; etc.
by F. R. Cohen, T. J. Lada, P. J. May - Springer
A thorough treatment of homology operations and of their application to the calculation of the homologies of various spaces. The book studies an up to homotopy notion of an algebra over a monad and its role in the theory of iterated loop spaces.
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.