- Theories related to elliptic curves
- 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 ...

- Bordism and cobordism theories
- 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 ...

- K-theories
- 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 ...

- Ordinary homology theories
- 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 ...

- 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 the spectru ...

- 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 othe ...

- Reciprocity law
- 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 ...

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