vector bundle

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vector bundle

Wikipedia

Noun

vector bundle (plural vector bundles)

1. (topology, category theory) A fiber bundle for which the fiber is a vector space.
   • 1995, Mauro Beltrametti, Andrew John Sommese, The Adjunction Theory of Complex Projective Varieties, Walter de Gruyter, page 8:

     Let E and F be two vector bundles on a compact algebraic set X.

   • 2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5,

     This solutions actually depend on the choice of a trivialisation ${\displaystyle \xi }$ of the universal family ${\displaystyle {\mathcal {P}}(n,d)}$ of stable vector bundles of rank ${\displaystyle n}$ and degree ${\displaystyle d}$.

   • 2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130:

     Definition 6.1.5 A non-zero vector bundle ${\displaystyle {\mathcal {F}}}$ on ${\displaystyle X}$ is said to be decomposable if it can be written as ${\displaystyle {\mathcal {F}}_{1}\oplus {\mathcal {F}}_{2}}$ with ${\displaystyle {\mathcal {F}}_{1}}$ and ${\displaystyle {\mathcal {F}}_{2}}$ non-zero vector bundles. Otherwise it is said to be indecomposable.

Hypernyms

• fiber bundle

Hyponyms

• tangent bundle

Meronyms

• zero section

Translations

Further reading

• Fiber bundle on Wikipedia.Wikipedia
• Coherent sheaf on Wikipedia.Wikipedia
• Holomorphic vector bundle on Wikipedia.Wikipedia
• vector bundle on nLab
• Vector Bundle on Wolfram MathWorld
• Vector bundle on Encylopedia of Mathematics
• Vector bundle, algebraic on Encylopedia of Mathematics
• Vector bundle, analytic on Encylopedia of Mathematics