American Journal of Mathematics
Buy Softcover. FAQ Policy. About this book Elliptic cohomology is an extremely beautiful theory with both geometric and arithmetic aspects. Show all. Table of contents 11 chapters Table of contents 11 chapters Introduction Pages Elliptic Genera Pages Work of M. Hopkins, N.
ISBN 13: 9780521700405
Kuhn, and D. Ravenel Pages Mathieu Groups Pages Cohomology of Certain Simple Groups Pages Completion Theorems Pages Elliptic Objects Pages KSp 0 X is the ring of stable equivalence classes of quaternionic vector bundles over X. G is some abelian group; for example the localization Z p at the prime p. Other K-theories can also be given coefficients. Introduced by Donald W. Anderson in his unpublished University of California, Berkeley Ph.
Coefficient ring: For ku, the coefficient ring is the ring of polynomials over Z on a single class v 1 in dimension 2.
This is a cohomology theory defined for spaces with involution, from which many of the other K-theories can be derived. Cobordism studies manifolds , where a manifold is regarded as "trivial" if it is the boundary of another compact manifold. The cobordism classes of manifolds form a ring that is usually the coefficient ring of some generalized cohomology theory. There are many such theories, corresponding roughly to the different structures that one can put on a manifold.
The functors of cobordism theories are often represented by Thom spaces of certain groups. Spectrum: S sphere spectrum. Stable homotopy is closely related to cobordism of framed manifolds manifolds with a trivialization of the normal bundle. Spectrum: MO Thom spectrum of orthogonal group. This was the first cobordism theory to be described completely.
Spectrum: MU Thom spectrum of unitary group. Spectrum: MSO Thom spectrum of special orthogonal group.https://iclanodi.tk
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Spectrum: MSU Thom spectrum of special unitary group. Spectrum: MSpin Thom spectrum of spin group. Coefficient ring: See D. Anderson, E.
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Spectrum: MSp Thom spectrum of symplectic group. The definition is similar to cobordism, except that one uses piecewise linear or topological instead of smooth manifolds , either oriented or unoriented.
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The coefficient rings are complicated. In fact MU p is a sum of suspensions of BP. They are named after Jack Morava. Coefficient ring Z 2 [ v 1 ,