Examples of 'vector bundles' in a sentence
Meaning of "vector bundles"
In mathematics, particularly in the field of algebraic topology, vector bundles refer to a construction where a space is associated with a vector space in a manner that varies smoothly from point to point. The concept of vector bundles is used to study the behavior of vector spaces within a given space
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- plural of vector bundle
How to use "vector bundles" in a sentence
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vector bundles
Vector bundles are often given more structure.
Such modules are also referred to as vector bundles.
Vector bundles are locally free.
The stability of these vector bundles has been studied.
Coherent sheaves can be seen as a generalization of vector bundles.
The deformation of these vector bundles has been studied.
Smooth functors may therefore be uniquely extended to functors defined on vector bundles.
Direct sum of vector bundles.
In algebraic geometry there is a similar theory of Chern classes of vector bundles.
Orientation of vector bundles.
The class of all vector bundles together with bundle morphisms forms a category.
And similarly for vector bundles.
Properties of certain vector bundles provide information about the underlying topological space.
They are topological invariants associated to vector bundles on a smooth manifold.
Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold.
See also
It applies to real vector bundles.
Ehresmann connection Vector bundles and covariant derivatives it is enough that the horizontal distribution satisfy.
They are topological invariants associated with vector bundles on a smooth manifold.
Two vector bundles with isomorphic associated gradeds are called S-equivalent.
The Porteous formula is a generalization to morphisms of vector bundles over a variety.
In particular, the vector bundles need not necessarily be complex.
We make use of heat equations associated to generalized Laplacians on vector bundles.
Serre also proved Serre duality for holomorphic vector bundles on any compact complex manifold.
The Euler class, in turn, relates to all other characteristic classes of vector bundles.
Moreover, we introduce the use of vector bundles framework in image processing.
Hermitian Yang-Mills connection and stable vector bundles.
In the following, we focus on real vector bundles in the category of topological spaces.
Using similar methods, we also obtain cancellation results for symplectic vector bundles of critical rank.
The stability of these vector bundles was studied in the case b=0.
On the other way, I prove vanishing theorems for ample vector bundles.
The vector bundles are exactly the torsion-free X-modules.
The Chern classes give a close connection between vector bundles and Chow groups.
Terng, C.L., Natural vector bundles and natural differential operators, Am.
Line bundles are both I-bundles and vector bundles of rank one.
Tate modules were introduced by Drinfeld ( 2006 ) to serve as a notion of infinite-dimensional vector bundles.
K-theory studies the isomorphism classes of all vector bundles over some topological space.
See also, analytic function, coherent sheaf and vector bundles.
Category, Vector bundles.
Let D { \ displaystyle D } be a ( possibly nonlinear ) differential operator between vector bundles of any rank.
This master 's thesis is concerned with symplectic vector bundles and their special subbundles.
There is also a quaternionic Pontryagin class, for vector bundles with quaternion structure.
Using linear algebra to classify vector bundles over P ^ 1.
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Vector bundles are often given more structure
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