See vector bundle in All languages combined, or Wiktionary
{
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"ref": "1995, Mauro Beltrametti, Andrew John Sommese, The Adjunction Theory of Complex Projective Varieties, Walter de Gruyter, page 8:",
"text": "Let E and F be two vector bundles on a compact algebraic set X.",
"type": "quote"
},
{
"text": "2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5,\nThis solutions actually depend on the choice of a trivialisation ξ of the universal family 𝒫(n,d) of stable vector bundles of rank n and degree d."
},
{
"ref": "2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130:",
"text": "Definition 6.1.5 A non-zero vector bundle #x5C;mathcal#x7B;F#x7D; on X is said to be decomposable if it can be written as #x5C;mathcal#x7B;F#x7D;#x5F;1#x5C;oplus#x5C;mathcal#x7B;F#x7D;#x5F;2 with #x5C;mathcal#x7B;F#x7D;#x5F;1 and #x5C;mathcal#x7B;F#x7D;#x5F;2 non-zero vector bundles. Otherwise it is said to be indecomposable.",
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"(topology, category theory) A fiber bundle for which the fiber is a vector space."
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"word": "vektorikimppu"
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"text": "2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5,\nThis solutions actually depend on the choice of a trivialisation ξ of the universal family 𝒫(n,d) of stable vector bundles of rank n and degree d."
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"ref": "2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130:",
"text": "Definition 6.1.5 A non-zero vector bundle #x5C;mathcal#x7B;F#x7D; on X is said to be decomposable if it can be written as #x5C;mathcal#x7B;F#x7D;#x5F;1#x5C;oplus#x5C;mathcal#x7B;F#x7D;#x5F;2 with #x5C;mathcal#x7B;F#x7D;#x5F;1 and #x5C;mathcal#x7B;F#x7D;#x5F;2 non-zero vector bundles. Otherwise it is said to be indecomposable.",
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Download raw JSONL data for vector bundle meaning in English (2.5kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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