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In mathematics, a bundle gerbe is a geometrical model of certain 1-gerbes with connection, or equivalently of a 2-class in Deligne cohomology. U ( 1 )
Bundle_gerbe
Construct in mathematics
They can be seen as an analogue of fibre bundles where the fibre is the classifying stack of a group. Gerbes provide a convenient, if highly abstract
Gerbe
Topics referred to by the same term
player Zéphirin Gerbe (1810-1890) French naturalist Gerbe's Vole (Microtus gerbei), a species of rodent in the family Cricetidae Bundle gerbe This disambiguation
Gerbe_(disambiguation)
Principal fiber bundle
classifies line bundle gerbes. Wang sequence "Is every orientable circle bundle principal? - MathOverflow". Chern, Shiing-shen (1977), "Circle bundles", Lecture
Circle_bundle
Mathematical theory
problem are nontrivial. K-theory (physics) Wess–Zumino–Witten model Bundle gerbe Donavan, Peter; Karoubi, Max (1970). "Graded Brauer groups and $K$-theory
Twisted_K-theory
compared with ordinary Deligne cohomology on complex analytic varieties. Bundle gerbe Motivic cohomology Hodge structure Intermediate Jacobian Hopkins, Michael
Deligne_cohomology
Infinite-dimensional group in topology
homotopy fiber. Gerbe N-group (category theory) Elliptic cohomology String bordism Jurco, Branislav (August 2011). "Crossed Module Bundle Gerbes; Classification
String_group
Type of vector bundle
In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav V. Nori, as the main tool in the construction
Essentially finite vector bundle
Essentially_finite_vector_bundle
denotes the magnetic field strength). Mathematically the B-field is a gerbe or bundle gerbe over spacetime, which means B {\displaystyle B} consists of a collection
Deformed Hermitian Yang–Mills equation
Deformed_Hermitian_Yang–Mills_equation
twisted Chern class defined in Twisted K-theory and the K-theory of Bundle Gerbes by Peter Bouwknegt, Alan L. Carey, Varghese Mathai, Michael K. Murray
Ramond–Ramond_field
Generalisation of a sheaf; a fibered category that admits effective descent
associated line bundle can be reconstructed. A gerbe is a stack in groupoids that is locally nonempty, for example the trivial gerbe B G {\displaystyle
Stack_(mathematics)
Correspondsnce between Higgs bundles and fundamental group representations
after Kevin Corlette and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
It is a generalization of the Lie bracket from an operation on the tangent bundle
from an operation on the tangent bundle to an operation on the direct sum of the tangent bundle and the vector bundle of p-forms. The case p = 1 {\displaystyle
Courant_bracket
Kind of complex manifold
\mathbb {Z} )} , to construct gerbes on a complex torus Block, Jonathan; Daenzer, Calder (2008). "Mukai duality for gerbes with connection". Crelle's Journal
Complex_torus
Descent (category theory) Grothendieck's Galois theory Algebraic stack Gerbe Étale cohomology Motive (algebraic geometry) Motivic cohomology A¹ homotopy
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Concept in differential geometry
X\to X} is a gerbe. A theorem of Giraud says that H 2 ( X , S 1 ) {\displaystyle H^{2}(X,S^{1})} corresponds one-to-one to the set of gerbes over X {\displaystyle
Differentiable_stack
French-American mathematician
conjectures with Masaki Kashiwara. He has also worked on gerbes, cyclic homology, Quillen bundles, and geometric class field theory, among other geometric
Jean-Luc_Brylinski
Chemical sensing cells in the intestinal lining
but still isolated. List of human cell types derived from the germ layers Gerbe F, Jay P (November 2016). "Intestinal tuft cells: epithelial sentinels linking
Tuft_cell
American supermarket chain
concert with the company's CFO and store manager. Skimmed cash was placed in bundles in Leonard Sr.'s office fireplace, to be later moved offshore or disguised
Stew_Leonard's
Generalization of (co)homology using chain complexes
hypercohomology spectral sequences are in the study of gerbes. Recall that rank n vector bundles on a space X {\displaystyle X} can be classified as the
Hyperhomology
Collection of Latin glosses on the Vulgate Bible
mât Occ. mast manipulos bundles.ACC PR. */maˈnʊkli/nom OFr. manoil OIt. manocchi Ro. mănuchi garbas Frankish *garba. Fr. gerbes Occ. garbas Cat. garbes
Reichenau_Glossary
American mathematician
the American Mathematical Society. With Tony Pantev: Torus fibrations, Gerbes and duality, Memoirs AMS 2008 Editor with Mauro Francaviglia: Integrable
Ron_Donagi
Generalization of algebraic spaces or schemes
presentation, the stack B G {\displaystyle BG} is algebraictheorem 6.1. Gerbe Chow group of a stack Cohomology of a stack Quotient stack Sheaf on an algebraic
Algebraic_stack
Abelian group related to division algebras
G m ) {\displaystyle H^{2}(X,G_{m})} can be viewed as classifying the gerbes over X {\displaystyle X} with structure group G m {\displaystyle G_{m}}
Brauer_group
group scheme G is a good quotient such that the fibers are orbits. gerbe A gerbe is (roughly) a stack that is locally nonempty and in which two objects
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Bundle of cereal-crop stems bound together after reaping
sheaf is called a garb, a term cognate with grab, grub, grave and German Gerbe. Omer (unit), a Biblical measure of volume of grain. Haystacks (Monet series)
Sheaf_(agriculture)
degrees 0 {\displaystyle 0} and 1 {\displaystyle 1} . ∞-groupoid n-group Gerbe Jibladze, Mamuka; Pirashvili, Teimuraz (2011-06-28). "Cohomology with coefficients
Abelian_2-group
Tool to track locally defined data attached to the open sets of a topological space
but probably should be attributed to a number of authors). Coherent sheaf Gerbe Stack (mathematics) Sheaf of spectra Perverse sheaf Presheaf of spaces Constructible
Sheaf_(mathematics)
Concept in ring theory
obstruction to the Hasse principle is defined using the Brauer group of schemes. Gerbe Class field theory Algebraic K-theory Motivic cohomology Norm residue isomorphism
Azumaya_algebra
ISSN 1609-3321, MR 1900583 Arkhipov, Sergey; Kremnizer, Kobi (2010), "2-gerbes and 2-Tate spaces", Arithmetic and geometry around quantization, vol. 279
Tate_vector_space
American multinational retail corporation
Retrieved December 16, 2012. "Walmart Pushing Limited $199 Kinect Pre-Order Bundle". PC World. July 14, 2010. Archived from the original on July 18, 2010.
Walmart
History of maths
manipulate morphisms in a monoidal category 1971 Jean Giraud Gerbes: Categorified principal bundles that are also special cases of stacks 1971 Joachim Lambek
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
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