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Surgery exact sequence

In the mathematical surgery theory, the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension > 4 {\displaystyle >4} . The surgery structure set S ( X ) {\displaystyle {\mathcal {S}}(X)} of a compact n {\displaystyle n} -dimensional manifold X {\displaystyle X} is a pointed set which…

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Definition

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Versions revisited

Classification of manifolds

Quinn's surgery fibration

Examples

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Surgery exact sequence

Nodes54
Edges53
Triples41
Avg. degree1.96
Density0.037037
Components1

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Surgery exact sequence

Top relations

related to Classification of manifolds · 10
Surgery exact sequence → Equivalently, Firstly, In, It, Let, Poincaré, Secondly, Spivak, The, This
related to 2. Topological spheres · 9
Surgery exact sequence → Freedman, From, In, It, Perelman, Poincaré, Smale, The, TOP
related to 1. Homotopy spheres · 5
Surgery exact sequence → In, Kervaire, Milnor, The, This
related to The exactness · 5
Surgery exact sequence → For, Hence, Im, Recall, So
related to Versions revisited · 5
Surgery exact sequence → In, Moreover, Note, Ranicki, This
related to Versions · 4
Surgery exact sequence → Another, One, PL, There
is a · 2
Surgery exact sequence → exact sequence in the following sense, main technical tool to calculate the surgery structure set of a compact manifold in dimension
related to Definition · 1
Surgery exact sequence → The

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Important terminology

displaystyle surgery mathcal normal sequence exact manifolds structure manifold pi homotopy one set topological l-groups obstruction maps map colon invariants

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Surgery exact sequenceis amain technical tool to calculate the surgery structure set of a compact manifold in dimension0.90text
Surgery exact sequenceis aexact sequence in the following sense0.90text
Surgery exact sequencerelated to 1. Homotopy spheresThis0.60section
Surgery exact sequencerelated to 1. Homotopy spheresThe0.60section
Surgery exact sequencerelated to 1. Homotopy spheresKervaire0.60section
Surgery exact sequencerelated to 1. Homotopy spheresMilnor0.60section
Surgery exact sequencerelated to 1. Homotopy spheresIn0.60section
Surgery exact sequencerelated to 2. Topological spheresThe0.60section
Surgery exact sequencerelated to 2. Topological spheresPoincaré0.60section
Surgery exact sequencerelated to 2. Topological spheresTOP0.60section
Surgery exact sequencerelated to 2. Topological spheresIt0.60section
Surgery exact sequencerelated to 2. Topological spheresSmale0.60section

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