Instantons and the Topology of 4-Manifolds
Identifieur interne : 000C02 ( Istex/Corpus ); précédent : 000C01; suivant : 000C03Instantons and the Topology of 4-Manifolds
Auteurs : Ronald J. SternSource :
Abstract
Abstract: Geometric topology is the study of metric spaces which are locally homeomorphic to Euclidean n-space R n ; that is, it studies topological (TOP) n-manifolds. The customary goal is to discover invariants, usually algebraic invariants, which classify all manifolds of a given dimension. This is separated into an existence question—finding an n-manifold with the given invariants—and a uniqueness question—determining how many n-manifolds have the given invariant. As is (and was) quickly discovered, TOP manifolds are too amorphous to study initially, so one adds structure which is compatible with the available topology and which broadens the available tools. Presumably, the richer the structure imposed on a manifold, the fewer objects one is forced to study.
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DOI: 10.1007/978-1-4613-0195-0_30
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The customary goal is to discover invariants, <Emphasis Type="Italic">usually</Emphasis> algebraic invariants, which classify all manifolds of a given dimension. This is separated into an existence question—finding an <Emphasis Type="Italic">n</Emphasis>-manifold with the given invariants—and a uniqueness question—determining how many <Emphasis Type="Italic">n</Emphasis>-manifolds have the given invariant. As is (and was) quickly discovered, TOP manifolds are too amorphous to study initially, so one adds structure which is compatible with the available topology and which broadens the available tools. 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The customary goal is to discover invariants, usually algebraic invariants, which classify all manifolds of a given dimension. This is separated into an existence question—finding an n-manifold with the given invariants—and a uniqueness question—determining how many n-manifolds have the given invariant. As is (and was) quickly discovered, TOP manifolds are too amorphous to study initially, so one adds structure which is compatible with the available topology and which broadens the available tools. 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