The diffeology of Milnor's classifying space

Autor: Jordan Watts, Jean-Pierre Magnot
Přispěvatelé: Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2017
Předmět:
Connection (fibred manifold)
Pure mathematics
Classifying space
[SHS.INFO]Humanities and Social Sciences/Library and information sciences
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
[MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA]
01 natural sciences
Mathematics - Geometric Topology
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]
Mathematics::Algebraic Geometry
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]
[NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Diffeology
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Classification theorem
[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]
0101 mathematics
[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
Mathematics::Symplectic Geometry
ComputingMilieux_MISCELLANEOUS
Mathematics
Discrete mathematics
Group (mathematics)
010102 general mathematics
Geometric Topology (math.GT)
Join (topology)
16. Peace & justice
Principal bundle
010101 applied mathematics
Universal bundle
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]
[SHS.GESTION]Humanities and Social Sciences/Business administration
Mathematics::Differential Geometry
Geometry and Topology
[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
Zdroj: Topology and its Applications
Topology and its Applications, Elsevier, 2017, 232, pp.189-213. ⟨10.1016/j.topol.2017.10.011⟩
ISSN: 0166-8641
Popis: We define a diffeology on the Milnor classifying space of a diffeological group $G$, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth principal bundles, we prove the existence of a diffeological connection on any principal bundle (with mild conditions on the bundles and groups), and apply the theory to some examples, including some infinite-dimensional groups, as well as irrational tori.
29 pages -- v3 fixes another error, and clarifies some comments on differential forms
Databáze: OpenAIRE
Externí odkaz: