In mathematics, particularly algebraic topology, cohomotopy sets are particular contravariant functors from the category of pointed topological spaces...
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Mapping cone (topology) Wedge sum Smash product Adjunction space Cohomotopy Cohomotopy group Brown's representability theorem Eilenberg–MacLane space Fibre...
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The theorem relates the Burnside ring of a finite group G to the stable cohomotopy of the classifying space BG. The conjecture was made in the mid 1970s...
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description of the stable cohomotopy theory of the classifying space of a finite group. It is the analogue for cohomotopy of the work of Michael Atiyah...
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property – Mathematical property Homology and cohomology Homotopy group and Cohomotopy group Knot invariant – Function of a knot that takes the same value for...
17 KB (2,428 words) - 07:40, 4 July 2024
\alpha } . A practical way of finding α {\displaystyle \alpha } is to use cohomotopy operator h {\displaystyle h} , that is a local inverse of δ {\displaystyle...
42 KB (6,824 words) - 21:45, 23 June 2024
Mathematical object (section Set theory)
Topological spaces Uniformities Manifolds Atlases Charts Cohomology groups Cohomotopy groups Homology groups Homotopy groups Knots Unknot Trefoil knot Holes...
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functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. In practice, there...
23 KB (3,271 words) - 09:41, 30 July 2024
complexes. Some examples of generalized cohomology theories are: Stable cohomotopy groups π S ∗ ( X ) . {\displaystyle \pi _{S}^{*}(X).} The corresponding...
43 KB (6,691 words) - 21:02, 23 March 2024
theory) cohomotopy group For a based space X, the set of homotopy classes [ X , S n ] {\displaystyle [X,S^{n}]} is called the n-th cohomotopy group of...
52 KB (7,629 words) - 12:07, 26 July 2024
coefficient ring of an extraordinary cohomology theory, called stable cohomotopy theory. The unstable homotopy groups (for n < k + 2) are more erratic;...
82 KB (7,972 words) - 00:30, 24 August 2024
absolute neighborhood retracts (ANRs), and the cohomotopy groups, later called Borsuk–Spanier cohomotopy groups; he also founded shape theory; Borsuk's...
123 KB (12,238 words) - 12:43, 28 August 2024