Whitehead group
Encyclopedia
Whitehead group in mathematics may mean:
All named after J. H. C. Whitehead
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- A group W with Ext(W, Z)=0; see Whitehead problemWhitehead problemIn group theory, a branch of abstract algebra, the Whitehead problem is the following question:Shelah proved that Whitehead's problem is undecidable within standard ZFC set theory.-Refinement:...
- For a ring, the Whitehead group Wh(A) of a ring A, equal to
- For a group, the Whitehead group Wh(G) of a group G, equal to K1(Z[G])/{±G}. Note that this is a quotient of the Whitehead group of the group ring.
- The Whitehead group Wh(A) of a simplicial complexSimplicial complexIn mathematics, a simplicial complex is a topological space of a certain kind, constructed by "gluing together" points, line segments, triangles, and their n-dimensional counterparts...
or PL-manifoldManifoldIn mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
A, equal to Wh(π1(A)); see Whitehead torsionWhitehead torsionIn geometric topology, the obstruction to a homotopy equivalence f\colon X \to Y of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion \tau, which is an element in the Whitehead group Wh. These are named after the mathematician J. H. C...
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All named after J. H. C. Whitehead
J. H. C. Whitehead
John Henry Constantine Whitehead FRS , known as Henry, was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai , in India, and died in Princeton, New Jersey, in 1960....
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