This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Cohomotopy set" – news · newspapers · books · scholar · JSTOR(July 2014) (Learn how and when to remove this message)
In mathematics, particularly algebraic topology, cohomotopy sets are particular contravariant functors from the category of pointed topological spaces and basepoint-preserving continuous maps to the category of sets and functions. They are dual to the homotopy groups, but less studied.
In mathematics, particularly algebraic topology, cohomotopysets are particular contravariant functors from the category of pointed topological spaces...
Mapping cone (topology) Wedge sum Smash product Adjunction space CohomotopyCohomotopy group Brown's representability theorem Eilenberg–MacLane space Fibre...
\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...
property – Mathematical property Homology and cohomology Homotopy group and Cohomotopy group Knot invariant – Function of a knot that takes the same value for...
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...
functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. In practice, there...
complexes. Some examples of generalized cohomology theories are: Stable cohomotopy groups π S ∗ ( X ) . {\displaystyle \pi _{S}^{*}(X).} The corresponding...
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...
coefficient ring of an extraordinary cohomology theory, called stable cohomotopy theory. The unstable homotopy groups (for n < k + 2) are more erratic;...
absolute neighborhood retracts (ANRs), and the cohomotopy groups, later called Borsuk–Spanier cohomotopy groups; he also founded shape theory; Borsuk's...
Global Information