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35 relations: Algebra, Algebraic K-theory, Brown–Peterson cohomology, C*-algebra, Cobordism, Cohomology, Commutative ring spectrum, Cup product, Elliptic cohomology, En-ring, Fiber bundle, Geometric topology, Hochschild homology, Homotopy, J. Peter May, Jacob Lurie, Limit (category theory), Loop space, Lubin–Tate formal group law, Model category, Monoid, Monoidal category, Morava K-theory, Operad theory, Quillen adjunction, Simplicial set, Smash product, Spectrum (topology), Stable homotopy theory, Steenrod algebra, Suspension (topology), Symmetric group, Symmetric spectrum, Thom space, Topological modular forms.
Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Algebraic K-theory
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory.
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Brown–Peterson cohomology
In mathematics, Brown–Peterson cohomology is a generalized cohomology theory introduced by, depending on a choice of prime p. It is described in detail by.
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C*-algebra
C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.
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Cobordism
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 (French bord, giving cobordism) of a manifold.
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Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.
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Commutative ring spectrum
In the mathematical field of algebraic topology, a commutative ring spectrum, roughly equivalent to a E_\infty-ring spectrum, is a commutative monoid in a good category of spectra.
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Cup product
In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring.
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Elliptic cohomology
In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology.
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En-ring
In mathematics, an \mathcal_n-algebra in a symmetric monoidal infinity category C consists of the following data.
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Fiber bundle
In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.
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Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
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Hochschild homology
In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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J. Peter May
Jon Peter May (born September 16, 1939 in New York) is an American mathematician, working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra.
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Jacob Lurie
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at Harvard University.
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Limit (category theory)
In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits.
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Loop space
In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, maps from the circle S1 to X, equipped with the compact-open topology.
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Lubin–Tate formal group law
In mathematics, the Lubin–Tate formal group law is a formal group law introduced by to isolate the local field part of the classical theory of complex multiplication of elliptic functions.
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Model category
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations'.
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Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
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Monoidal category
In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.
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Morava K-theory
In stable homotopy theory, a branch of mathematics, Morava K-theory is one of a collection of cohomology theories introduced in algebraic topology by Jack Morava in unpublished preprints in the early 1970s.
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Operad theory
Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity.
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Quillen adjunction
In homotopy theory, a branch of mathematics, a Quillen adjunction between two closed model categories C and D is a special kind of adjunction between categories that induces an adjunction between the homotopy categories Ho(C) and Ho(D) via the total derived functor construction.
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Simplicial set
In mathematics, a simplicial set is an object made up of "simplices" in a specific way.
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Smash product
In mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) X and Y is the quotient of the product space X × Y under the identifications (x, y0) ∼ (x0, y) for all x ∈ X and y ∈ Y.
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Spectrum (topology)
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory.
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Stable homotopy theory
In mathematics, stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.
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Steenrod algebra
In algebraic topology, a Steenrod algebra was defined by to be the algebra of stable cohomology operations for mod p cohomology.
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Suspension (topology)
In topology, the suspension SX of a topological space X is the quotient space: of the product of X with the unit interval I.
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Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
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Symmetric spectrum
In algebraic topology, a symmetric spectrum X is a spectrum of pointed simplicial sets that comes with an action of the symmetric group \Sigma_n on X_n such that the composition of structure maps is equivariant with respect to \Sigma_p \times \Sigma_n.
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Thom space
In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.
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Topological modular forms
In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory.
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Redirects here:
E infinity ring spectrum, E-infinity ring, E-infinity ring spectrum, S-modules.
References
[1] https://en.wikipedia.org/wiki/Highly_structured_ring_spectrum
