Examples of 'k-theory' in a sentence
Meaning of "k-theory"
k-theory (noun) - K-theory is a mathematical concept within the field of algebraic topology and abstract algebra. It deals with studying and classifying vector bundles and projective modules over topological spaces or schemes. This term is used in academic and research contexts among mathematicians, scholars, and students specializing in algebraic geometry or related disciplines
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- The study of rings R generated by the set of vector bundles over some topological space or scheme; (dated, obsolete) that part of algebraic topology comprising what is now called topological K-theory.
- The study of rings R generated by the set of vector bundles over some topological space or scheme;
- that part of algebraic topology comprising what is now called topological K-theory.
- The cohomology generated by the set of vector bundles over some topological space or scheme.
How to use "k-theory" in a sentence
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k-theory
K-theory studies the isomorphism classes of all vector bundles over some topological space.
His thesis was in the area of equivariant K-theory.
Similarly algebraic K-theory relies in a way on classifying spaces of groups.
Adams was also a pioneer in the application of K-theory.
Algebraic K-theory is related to the group of invertible matrices with coefficients the given field.
The remaining discussion is focussed on complex K-theory.
FGQ scientists extended previous results to K-theory classes of general representations.
This example is useful in algebraic K-theory.
K-theory of finite groups and orders.
These types of examples appear in K-theory.
In mathematics, topological K-theory is a branch of algebraic topology.
This result has important uses in topological K-theory.
In this work we study algebraic and topological k-theory and the k-theory of c * - algebras.
Barwick has also made contributions to algebraic K-theory.
For example, a complex K-theory is a ring spectrum.
See also
In algebraic topology it is an extraordinary cohomology theory known as topological K-theory.
It is special among the various twists that K-theory admits for two reasons.
Waldhausen and biWaldhausen categories are linked with algebraic K-theory.
However Chern characters are always rational, and so the K-theory classification must be replaced.
It is studied in its own right as an object of geometric interest in K-theory.
The two most famous applications of topological K-theory are both due to Frank Adams.
The most common application of the plus construction is in algebraic K-theory.
For this, algebraic K-theory had to be reformulated.
He subsequently found a much shorter proof using cohomology operations in K-theory.
Much of his recent work has concerned equivariant algebraic K-theory and equivariant homotopy theory.
Algebraic cycles have also been shown to be closely connected with algebraic K-theory.
In mathematics, K-theory is a tool used in several disciplines.
The motivation for this notion comes from algebraic K-theory of rings.
Homogeneous spaces, algebraic K-theory and cohomological dimension of fields.
This is not a meaningful mathematical statement, but a metaphor expressing an analogy with algebraic K-theory.
Finally, we study the hermitian K-theory of number fields.
We define an index class in Kasparov bivariant K-theory.
As a first example, note that the K-theory of a point are the integers.
There followed a period in which there were various partial definitions of higher K-theory functors.
The K-theory and the index theorem.
Polylogarithm ladders occur naturally and deeply in K-theory and algebraic geometry.
The K-theory spectrum of a ring is an example of an Ω-spectrum.
This theory is not yet a finished product - and more recent trends have used K-theory approaches.
A third construction of K-theory groups is the S-construction, due to Waldhausen.
Her PhD advisor was John Wagoner and her doctoral thesis was on algebraic K-theory.
In later work he contributed to algebraic K-theory Birch-Tate conjecture.
Using this new theory, he proved the Theorem of the Heart for Waldhausen K-theory.
For example, the spectrum of topological K-theory is a ring spectrum.
His doctoral students at Chicago include Charles Weibel, also known for his work in K-theory.
He solved the Strong approximation problem, developed the reduced K-theory and solved the Tannaka-Artin problem.
In algebraic topology, it is a cohomology theory known as topological K-theory.
Relative K-theory class.
This is the defining relation of Milnor K-theory.
K-theory and cobordism are the best-known.
Daniel Quillen formulates higher algebraic K-theory.
