Faster access than browser!Similarities between Algebraic K-theory and Cohomology
Algebraic K-theory and Cohomology have 45 things in common (in Unionpedia): Abstract algebra, Alexander Grothendieck, Birkhäuser, Cambridge University Press, Characteristic class, Chern class, Commutative ring, Compact space, Continuous function, CW complex, Cyclic homology, Daniel Quillen, Derived category, Differential form, Eilenberg–Steenrod axioms, Exact sequence, Excision theorem, Exterior algebra, Field (mathematics), Finitely generated module, Free module, Galois cohomology, Geometry, Graded ring, Graded-commutative ring, Henri Poincaré, Hochschild homology, Homotopy, Homotopy group, Ideal (ring theory), ..., Integer, Intersection theory, K-theory, Motivic cohomology, Noetherian ring, Princeton University Press, Real number, Ring (mathematics), Sheaf (mathematics), Simplicial complex, Spectrum (topology), Springer Science+Business Media, Topology, Vector bundle, Vector space. Expand index (15 more) »
Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
Abstract algebra and Algebraic K-theory · Abstract algebra and Cohomology ·
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
Alexander Grothendieck and Algebraic K-theory · Alexander Grothendieck and Cohomology ·
Birkhäuser
Birkhäuser is a former Swiss publisher founded in 1879 by Emil Birkhäuser.
Algebraic K-theory and Birkhäuser · Birkhäuser and Cohomology ·
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
Algebraic K-theory and Cambridge University Press · Cambridge University Press and Cohomology ·
Characteristic class
In mathematics, a characteristic class is a way of associating to each principal bundle X a cohomology class of X. The cohomology class measures the extent the bundle is "twisted" — and whether it possesses sections.
Algebraic K-theory and Characteristic class · Characteristic class and Cohomology ·
Chern class
In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles.
Algebraic K-theory and Chern class · Chern class and Cohomology ·
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
Algebraic K-theory and Commutative ring · Cohomology and Commutative ring ·
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Algebraic K-theory and Compact space · Cohomology and Compact space ·
Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
Algebraic K-theory and Continuous function · Cohomology and Continuous function ·
CW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.
Algebraic K-theory and CW complex · CW complex and Cohomology ·
Cyclic homology
In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds.
Algebraic K-theory and Cyclic homology · Cohomology and Cyclic homology ·
Daniel Quillen
Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician.
Algebraic K-theory and Daniel Quillen · Cohomology and Daniel Quillen ·
Derived category
In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes.
Algebraic K-theory and Derived category · Cohomology and Derived category ·
Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
Algebraic K-theory and Differential form · Cohomology and Differential form ·
Eilenberg–Steenrod axioms
In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common.
Algebraic K-theory and Eilenberg–Steenrod axioms · Cohomology and Eilenberg–Steenrod axioms ·
Exact sequence
An exact sequence is a concept in mathematics, especially in group theory, ring and module theory, homological algebra, as well as in differential geometry.
Algebraic K-theory and Exact sequence · Cohomology and Exact sequence ·
Excision theorem
In algebraic topology, a branch of mathematics, the excision theorem is a theorem about relative homology—given topological spaces X and subspaces A and U such that U is also a subspace of A, the theorem says that under certain circumstances, we can cut out (excise) U from both spaces such that the relative homologies of the pairs (X,A) and (X \ U,A \ U) are isomorphic.
Algebraic K-theory and Excision theorem · Cohomology and Excision theorem ·
Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
Algebraic K-theory and Exterior algebra · Cohomology and Exterior algebra ·
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
Algebraic K-theory and Field (mathematics) · Cohomology and Field (mathematics) ·
Finitely generated module
In mathematics, a finitely generated module is a module that has a finite generating set.
Algebraic K-theory and Finitely generated module · Cohomology and Finitely generated module ·
Free module
In mathematics, a free module is a module that has a basis – that is, a generating set consisting of linearly independent elements.
Algebraic K-theory and Free module · Cohomology and Free module ·
Galois cohomology
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups.
Algebraic K-theory and Galois cohomology · Cohomology and Galois cohomology ·
Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
Algebraic K-theory and Geometry · Cohomology and Geometry ·
Graded ring
In mathematics, in particular abstract algebra, a graded ring is a ring that is a direct sum of abelian groups R_i such that R_i R_j \subseteq R_.
Algebraic K-theory and Graded ring · Cohomology and Graded ring ·
Graded-commutative ring
In algebra, a graded-commutative ring (also called a skew-commutative ring) is a graded ring that is commutative in the graded sense; that is, homogeneous elements x, y satisfy where |x|, |y| denote the degrees of x, y. A commutative (non-graded) ring, with trivial grading, is a basic example.
Algebraic K-theory and Graded-commutative ring · Cohomology and Graded-commutative ring ·
Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
Algebraic K-theory and Henri Poincaré · Cohomology and Henri Poincaré ·
Hochschild homology
In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings.
Algebraic K-theory and Hochschild homology · Cohomology and Hochschild homology ·
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.
Algebraic K-theory and Homotopy · Cohomology and Homotopy ·
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.
Algebraic K-theory and Homotopy group · Cohomology and Homotopy group ·
Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
Algebraic K-theory and Ideal (ring theory) · Cohomology and Ideal (ring theory) ·
Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
Algebraic K-theory and Integer · Cohomology and Integer ·
Intersection theory
In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring.
Algebraic K-theory and Intersection theory · Cohomology and Intersection theory ·
K-theory
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme.
Algebraic K-theory and K-theory · Cohomology and K-theory ·
Motivic cohomology
Motivic cohomology is an invariant of algebraic varieties and of more general schemes.
Algebraic K-theory and Motivic cohomology · Cohomology and Motivic cohomology ·
Noetherian ring
In mathematics, more specifically in the area of abstract algebra known as ring theory, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; that is, given any chain of left (or right) ideals: there exists an n such that: Noetherian rings are named after Emmy Noether.
Algebraic K-theory and Noetherian ring · Cohomology and Noetherian ring ·
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
Algebraic K-theory and Princeton University Press · Cohomology and Princeton University Press ·
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
Algebraic K-theory and Real number · Cohomology and Real number ·
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
Algebraic K-theory and Ring (mathematics) · Cohomology and Ring (mathematics) ·
Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
Algebraic K-theory and Sheaf (mathematics) · Cohomology and Sheaf (mathematics) ·
Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
Algebraic K-theory and Simplicial complex · Cohomology and Simplicial complex ·
Spectrum (topology)
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory.
Algebraic K-theory and Spectrum (topology) · Cohomology and Spectrum (topology) ·
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
Algebraic K-theory and Springer Science+Business Media · Cohomology and Springer Science+Business Media ·
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
Algebraic K-theory and Topology · Cohomology and Topology ·
Vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X.
Algebraic K-theory and Vector bundle · Cohomology and Vector bundle ·
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
Algebraic K-theory and Vector space · Cohomology and Vector space ·
The list above answers the following questions
- What Algebraic K-theory and Cohomology have in common
- What are the similarities between Algebraic K-theory and Cohomology
Algebraic K-theory and Cohomology Comparison
Algebraic K-theory has 182 relations, while Cohomology has 186. As they have in common 45, the Jaccard index is 12.23% = 45 / (182 + 186).
References
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