### A History of Algebraic and Differential Topology, 1900 - 1960 (Modern Birkhäuser Classics)

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Homotopy Theoretic Methods in Group Cohomology. Topology from the Differentiable Viewpoint. Princeton Univer- sity Press, Just 65 pages, so only a small amount of material is covered, alas. Morse Theory. Lectures on the h-Cobordism Theorem.

An Introduction to Morse Theory. Differential Manifolds. Academic Press, Dover reprint, Perhaps the price had something to do with this. Fortunately there is now an inexpensive Dover reprint. Piecewise Linear Topology.

PL topology was popular in the early days of manifold theory, but with the develop- ment of the appropriate tools in the purely topological category the PL category has fallen out of favor. The best source for this classical subject seems to be:. Introduction to Piecewise-Linear Topology.

A textbook exposition is still lacking here, probably because of the technical difficulty of the subject. Here are an early monograph and a recent survey article:. Piecewise Linear Structures on Topological Manifolds.

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Surgery theory addresses the basic problem of classifying manifolds up to homeo- morphism or diffeomorphism. The first pages of the following book give a nice overview:. The Topological Classification of Stratified Spaces. Algebraic and Geometric Surgery.

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Oxford University Press, Surveys on Surgery Theory. Surgery on Compact Manifolds, 2nd ed. One of the classic early papers could also serve rather well to give the flavor of surgery theory:. Groups of homotopy spheres. Annals of Mathematics 77 , Someone should someday write a comprehensive exposition of topological surface theory.

A small fraction of the theory can be found in. Automorphisms of Surfaces after Nielsen and Thurston. LMS Student Texts 9. On the geometry and dynamics of diffeomorphisms of surfaces. Three-Dimensional Geometry and Topology. Also useful for the geometry of surfaces.

Basic Topology of 3-Manifolds. Geometries of 3-manifolds. London Math. Invariants for Homology 3-Spheres. Hyperbolic Manifolds and Discrete Groups. This is a very accessible topic and there are plenty of readable books. The following ones are listed more or less in order of increasing sophistication. Knot Theory. Carus Mathematical Monographs Mathematical Association of America, Knots and Links. Publish or Perish, Recently reprinted by the AMS. Still useful for the more classical theory.

Knots, Links, Braids and 3-Manifolds. Emphasizes ideas and intuition. Topology of 4-Manifolds. Using the Borsuk-Ulam Theorem. Highly readable and highly recommended. A History of Algebraic and Differential Topology Handbook of Geometric Topology. Finally, here are four classics that are included in this list mainly for their historical interest:.

Foundations of Algebraic Topology. Princeton Uni- versity Press, McGraw-Hill, Reprinted by Springer.

### Spheres, homotopy groups of the - Encyclopedia of Mathematics

Homology Theory. Contains some interesting unsuccessful attempts at reforming terminology and notation. The Topology of Fiber Bundles.

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Still quite readable. Read Free For 30 Days. Topology Books - Allen Hatcher. Description: Allen Hatcher gives his favourite books in various branches of topology, with short comments. Flag for inappropriate content. Related titles. Carousel Previous Carousel Next. Mariano R. Topology Course Lecture Notes - A.

McCluskey B.

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Jump to Page. Search inside document. Algebraic Topology III. Manifold Theory IV. Low-Dimensional Topology V. Miscellaneous I. Introductory Books. General Introductions. Intuitive Topology. American Mathematical Society The Shape of Space. Marcel Dekker, Basic Topology. On Thom Spectra, Orientability, and Cobordism.