Notation S = π = S0 is the sphere spectrum.Sn is the spectrum of the n-dimensional sphereSnY = Sn∧Y is the nth suspension of a spectrum Y. is the abelian group of morphisms from the spectrum X to th ...
Topological modular formsSpectra: tmf, TMF (previously called eo2.)The coefficient ring π*(tmf) is called the ring of topological modular forms. TMF is tmf with the 24th power of the modular form Δ ...
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 ...
The simpler K-theories of a space are often related to vector bundles over the space, and different sorts of K-theories correspond to different structures that can be put on a vector bundle.Real K-the ...
These are the theories satisfying the "dimension axiom" of the Eilenberg–Steenrod axioms that the homology of a point vanishes in dimension other than 0. They are determined by an abelian coefficient ...
S = π = S0 is the sphere spectrum.Sn is the spectrum of the n-dimensional sphereSnY = Sn∧Y is the nth suspension of a spectrum Y. is the abelian group of morphisms from the spectrum X to the spectru ...
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 othe ...
In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity.There are several different ways to express reciprocity laws. The early reciprocity laws found in the 19th cen ...
Some algebraic structures find uses in disciplines outside of abstract algebra. The following is meant to demonstrate some specific applications in other fields.In Physics:Lie groups are used extensiv ...
There are many examples of mathematical structures where algebraic structure exists alongside non-algebraic structure.Topological vector spaces are vector spaces with a compatible topology.Lie groups: ...
In full generality, an algebraic structure may use any number of sets and any number of axioms in its definition. The most commonly studied structures, however, usually involve only one or two sets an ...
Algebraic structures appear in most branches of mathematics, and students can encounter them in many different ways.Beginning study: In American universities, groups, vector spaces and fields are gene ...
In mathematics, there are many types of algebraic structures which are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may ...
