Topology Lecture Notes
by Thomas Ward
Publisher: UEA 2001
Number of pages: 88
Contents: Topological and Metric Spaces, Homotopy Exquivalence, Fundamental Groups, Covering Spaces and Applications, Classification of Surfaces, Simplicial Complexes and Homology Groups, Homology Calculations, Simplicial Approximation, Homological Algebra and the Exact Sequence of a Pair.
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by J. P. May - Springer
A paper devoted to the study of iterated loop spaces. Our goal is to develop a simple and coherent theory which encompasses most of the known results about such spaces. We begin with some history and a description of the desiderata of such a theory.
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.
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Contents: Important examples of topological spaces; Constructions; Homotopy and homotopy equivalence; CW-complexes and homotopy; Fundamental group; Covering spaces; Higher homotopy groups; Fiber bundles; Suspension Theorem and Whitehead product; etc.
by Danny Calegari - Mathematical Society of Japan
This is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology.