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Everything about Vector bundle
Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space : to every point of the space we associate a vector space in such a way that these vector spaces fit together to form another space of the same kind as, which is then called a vector bundle over . Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Vector bundleA 5-minute orientation
- Skim a recent paper: Fixed Points of Automorphisms of the Vector Bundle Moduli Space Over a Compact Riemann SurfaceInfluential work since 2022
- Pick up a classic book: Vector bundles on complex projective spacesThe most-reprinted book on the subject
- Read the landmark paper: Superpotentials for vector bundle moduliCited 71 times
- Go sideways: Fiber bundleA closely related topic
- Go sideways: Principal bundleA closely related topic
📖 Definitions
Noun A fiber bundle for which the fiber is a vector space.
🏆 Landmark papers (most cited)
Superpotentials for vector bundle moduli
Spanning forests and the vector bundle Laplacian
Vector Bundle Moduli and Small Instanton Transitions
The Atiyah class of a dg-vector bundle
Brauer obstruction for a universal vector bundle
Vector supersymmetry in the universal bundle
A vector bundle characterization of pn
Generalised connections over a vector bundle map
🆕 Influential since 2022
Fixed Points of Automorphisms of the Vector Bundle Moduli Space Over a Compact Riemann Surface
Relativistic massive particle with spin-1/2: A vector bundle point of view
Conformal vector fields and geometric solitons on the tangent bundle with the ciconia metric
Multiplicative vector fields on bundle gerbes
Higgs bundles twisted by a vector bundle
📚 Books worth reading
Vector bundles on complex projective spacesM. Schneider, Heinz Spindler · 1988
Moduli spaces and vector bundlesSteven B. Bradlow, S. Ramanan · 2009
Vector bundles in algebraic geometryN. J. Hitchin, P. E. Newstead · 1995
SyzygiesE. Graham Evans · 1985
Vector Bundles and Differential EquationsAndre Hirschowitz · 1980- 📕Harmonic analysis on homogeneous spacesNolan R. Wallach · 1973
Helices and vector bundlesA. N. Rudakov · 1990- 📕Systèmes cohérents et structures de niveauJoseph Le Potier · 1993
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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