cobordism ring

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• Cobordism — A cobordism (W;M,N). In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold. Two manifolds are cobordant if their disjoint… …   Wikipedia

• Complex cobordism — In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using… …   Wikipedia

• Chow ring — In algebraic geometry, the Chow ring (named after W. L. Chow) of an algebraic variety is an algebraic geometric analogue of the cohomology ring of the variety considered as a topological space: its elements are formed out of actual subvarieties… …   Wikipedia

• List of cohomology theories — This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at… …   Wikipedia

• Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) …   Wikipedia

• Genus of a multiplicative sequence — In mathematics, the genus of a multiplicative sequence is a ring homomorphism, from the cobordism ring of smooth oriented compact manifolds to another ring, usually the ring of rational numbers.DefinitionA genus phi; assigns a number phi;( X ) to …   Wikipedia

• Adams spectral sequence — In mathematics, the Adams spectral sequence is a spectral sequence introduced by Adams (1958). Like all spectral sequences, it is a computational tool; it relates homology theory to what is now called stable homotopy theory. It is a… …   Wikipedia

• List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

• Low-dimensional topology — In mathematics, low dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3 manifolds and 4 manifolds, knot theory, and braid groups. It can be… …   Wikipedia

• Dold manifold — In mathematics, a Dold manifold is one of the manifolds P(m,n) = (Sm×CPn)/τ (where τ acts as −1 on the sphere Sm and a complex conjugation on complex projective space CPn) constructed by Dold (1956) that he used to give explicit generators… …   Wikipedia

• Whitehead torsion — In mathematics, Whitehead torsion is an invariant of an h cobordism in a Whitehead group, that is important in simple homotopy theory and surgery theory. It is named for J. H. C. Whitehead.Whitehead torsionSuppose that W is an h cobordism from M… …   Wikipedia