Homotopy, Homology, and Manifolds
The development of algebraic topology in the 1950's and 1960's was deeply influenced by the work of Milnor. In this collection of papers the reader finds those original papers and some previously unpublished works. The book is divided into four parts: Homotopy Theory, Homology and Cohomology, Manifolds, and Expository Papers. Introductions to each part provide some historical context and subsequent development. Of particular interest are the articles on classifying spaces, the Steenrod algebra, the introductory notes on foliations and the surveys of work on the Poincare conjecture. Together with the previously published volumes I-III of the Collected Works by John Milnor, volume IV provides a rich portion of the most important developments in geometry and topology from those decades. This volume is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing.
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ˇCech cohomology 2-sphere 3-manifolds abelian algebraic topology Amer Annals Math Annals of Math Axiom canonical classifying space cobordism codimension codimension q foliation completes the proof construction Corollary corresponding countable Cr-smooth curvature CW-complex deﬁne defined Definition denote diffeomorphism differentiable structure dimension dimensional embedded Euclidean space example fiber fibration finite foliating map foliation F functor fundamental group geometric given Haefliger Hence homeomorphic homology theory homotopy classes homotopy equivalence homotopy groups homotopy type Hopf Hq(X integrable homotopy invariant inverse limit isomorphic isomorphism-germ J. H. C. Whitehead John Milnor l-plane leaf Lemma map f Mathematics microbundle neighborhood normal bundle orientable pair piecewise linear PL-homeomorphism PL-microbundle Poincaré conjecture Pontrjagin classes Princeton Proc proof of Theorem proved Ricci flow Riemannian simplex simplicial complex smooth manifold smoothable sphere Steenrod homology subset tangent bundle Thurston topological manifold torus total space transverse triangulation trivial unique vector bundle Whitehead zero