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Everything about Principal bundle
Fiber bundle whose fibers are group torsors
In the mathematical area of topology, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product of a topological space with a group, but without requiring a product structure. In the same way as with the Cartesian product, a principal bundle is equipped withAn action of on, analogous to for a product space, where is an element of and is the group element from. A projection onto. For a product space, this is just the projection onto the first factor,. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Principal bundleA 5-minute orientation
- Skim a recent paper: Principal component analysis of vibration response of a rod bundle subjected to jet cross-flowInfluential work since 2022
- Pick up a classic book: Topology, Geometry, and Gauge FieldsThe most-reprinted book on the subject
- Read the landmark paper: On Invariant Connections over a Principal Fibre BundleCited 94 times
- Go sideways: Vector bundleA closely related topic
- Go sideways: Fiber bundleA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On Invariant Connections over a Principal Fibre Bundle
Connections and Higgs fields on a principal bundle
Monodromy group for a strongly semistable principal bundle over a curve
Harder–Narasimhan reduction of a principal bundle
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
The Principal Floquet Bundle and Exponential Separation for Linear Parabolic Equations
Classification of principal bundles and lie groupoids with prescribed gauge group bundle
Bundle formation of principal fibers in rat molars
🆕 Influential since 2022
Principal component analysis of vibration response of a rod bundle subjected to jet cross-flow
The principal Floquet bundle and the dynamics of fast diffusing communities
The principal bundle structure of continuum mechanics
Atiyah sequence and gauge transformations of a principal 2-bundle over a Lie groupoid
The Evolution of the Universe Based on Principal Bundle Geometry
📚 Books worth reading
Topology, Geometry, and Gauge FieldsGregory L. Naber · 1997
Principal BundlesStephen Bruce Sontz · 2015
Affine Flag Manifolds and Principal BundlesAlexander Schmitt · 2010
Small-format aerial photographyJames S. Aber · 2010- 📕North American Indian mythologyCottie Arthur Burland · 1968
- 📕Principal BundlesStephen B. Sontz · 2015
Affine flag manifolds and principal bundlesAlexander H. W. Schmitt · 2010- 📕Cohomology of principal bundles in semisimplicial theoryChristopher Watkiss · 1975
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Vector bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X…
- Fiber bundle In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally…
- G-structure on a manifold In differential geometry, a G-structure on an n {\displaystyle n} -manifold M {\displaystyle M} , for a given structure group G {\displaystyle G} , is…
- Frame bundle In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber…
- Associated bundle In mathematics, the theory of fiber bundles with a structure group G {\displaystyle G} (a topological group) allows an operation of creating an associated…
- Ehresmann connection In differential geometry, an Ehresmann connection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of…
- Glossary of differential geometry and topology This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related: Glossary of…
- Connection (principal bundle) In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle;…