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Topic

Extension topology

About: Extension topology is a(n) research topic. Over the lifetime, 1724 publication(s) have been published within this topic receiving 51458 citation(s).


Papers
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Book
01 Jan 1984
TL;DR: Elements of Algebraic Topology provides the most concrete approach to the subject with coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorem of point-set topology.
Abstract: Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.

2,646 citations

Book
01 Jan 1979

1,937 citations

Journal ArticleDOI
Abstract: © Publications mathématiques de l’I.H.É.S., 1977, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

1,559 citations

Book
01 Jan 1979

1,484 citations

Journal ArticleDOI
Abstract: 0. Introduction Manifold topology enjoyed a golden age in the late 1950's and 1960's. Of the mysteries still remaining after that period of great success the most compelling seemed to lie in dimensions three and four. Although experience suggested that manifold theory at these dimensions has a distinct character, the dream remained since my graduate school days that some key principle from the high dimensional theory would extend, at least to dimension four, and bring with it the beautiful adherence of topology to algebra familiar in dimensions greater than or equal to five. There is such a principle. It is a homotopy theoretic criterion for imbedding (relatively) a topological 2-handle in a smooth four-dimensional manifold with boundary. The main impact, as outlined in §1, is to the classification of 1-connected 4-manifolds and topological end recognition. However, certain applications to nonsimply connected problems such as knot concordance are also obtained. The discovery of this principle was made in three stages. From 1973 to 1975 Andrew Casson developed his theory of "flexible handles". These are certain pairs having the proper homotopy type of the common place open 2-handle H = (D X D, dD X D) but "flexible" in the sense that finding imbeddings is rather easy; in fact imbedding is implied by a homotopy theoretic criterion. It was clear to Casson that: (1) no known invariant—link theoretic

1,461 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20201
20192
20189
201770
201687
201577