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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[universal connection]] (just to record the references for the moment)

   stub for universal connection (just to record the references for the moment)

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 26th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Mark Mostow]], _The differentiable space structures of Milnor classifying spaces, simplicial complexes, and geometric realizations_, J. Differential Geom. Volume 14, Number 2 (1979), 255-293 ([euclid:jdg/1214434974](https://projecteuclid.org/euclid.jdg/1214434974)) <a href="https://ncatlab.org/nlab/revision/diff/universal+connection/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/universal+connection/2">v2</a>, <a href="https://ncatlab.org/nlab/show/universal+connection">current</a>

   added pointer to:

   • Mark Mostow, The differentiable space structures of Milnor classifying spaces, simplicial complexes, and geometric realizations, J. Differential Geom. Volume 14, Number 2 (1979), 255-293 (euclid:jdg/1214434974)

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have divided the References-section into subsection "In bounded dimension" and "In unbounded dimension". Then to the first of these I have added these pointers: *** Universal connections for manifolds of some bounded dimension $\leq n$ are appealed to in * {#Chern50} [[Shiing-shen Chern]], _Differential geometry of fiber bundles_, in: Proceedings of the International Congress of Mathematicians, Cambridge, Mass., (August-September 1950), vol. 2, pages 397-411, Amer. Math. Soc., Providence, R. I. (1952) ([[Chern-DifferentialGeometryOfFiberBundles.pdf:file]], [full proceedings vol 2 pdf](https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1950.2/ICM1950.2.ocr.pdf)) (in the context of [[Chern-Weil theory]]) and discussed in detail in * [[Mudumbai Narasimhan]] and [[Sundararaman Ramanan]], _Existence of Universal Connections_, American Journal of Mathematics Vol. 83, No. 3 (Jul., 1961), pp. 563-572 ([jstor:2372896 ](https://www.jstor.org/stable/2372896 )) * [[Mudumbai Narasimhan]] and [[Sundararaman Ramanan]], _Existence of Universal Connections II_, American Journal of Mathematics Vol. 85, No. 2 (Apr., 1963), pp. 223-231 ([jstor:2373211](https://www.jstor.org/stable/2373211)) * [[Roger Schlafly]], _Universal connections_, Invent Math 59, 59–65 (1980) ([doi:10.1007/BF01390314](https://doi.org/10.1007/BF01390314)) * [[Roger Schlafly]], _Universal connections: the local problem_, Pacific J. Math. Volume 98, Number 1 (1982), 157-171 ([euclid:pjm/1102734394](https://projecteuclid.org/euclid.pjm/1102734394)) <a href="https://ncatlab.org/nlab/revision/diff/universal+connection/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/universal+connection/3">v3</a>, <a href="https://ncatlab.org/nlab/show/universal+connection">current</a>

   I have divided the References-section into subsection “In bounded dimension” and “In unbounded dimension”. Then to the first of these I have added these pointers:

   ---

   Universal connections for manifolds of some bounded dimension $\leq n$ are appealed to in

   • {#Chern50} Shiing-shen Chern, Differential geometry of fiber bundles, in: Proceedings of the International Congress of Mathematicians, Cambridge, Mass., (August-September 1950), vol. 2, pages 397-411, Amer. Math. Soc., Providence, R. I. (1952) (Chern-DifferentialGeometryOfFiberBundles.pdf:file, full proceedings vol 2 pdf)

     (in the context of Chern-Weil theory)

   and discussed in detail in

   • Mudumbai Narasimhan and Sundararaman Ramanan, Existence of Universal Connections, American Journal of Mathematics Vol. 83, No. 3 (Jul., 1961), pp. 563-572 (jstor:2372896 )

   • Mudumbai Narasimhan and Sundararaman Ramanan, Existence of Universal Connections II, American Journal of Mathematics Vol. 85, No. 2 (Apr., 1963), pp. 223-231 (jstor:2373211)

   • Roger Schlafly, Universal connections, Invent Math 59, 59–65 (1980) (doi:10.1007/BF01390314)

   • Roger Schlafly, Universal connections: the local problem, Pacific J. Math. Volume 98, Number 1 (1982), 157-171 (euclid:pjm/1102734394)

   diff, v3, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso pointer to * Shrawan Kumar, _A Remark on Universal Connections_, Mathematische Annalen 260 (1982): 453-462 ([dml:163680](http://eudml.org/doc/163680)) <a href="https://ncatlab.org/nlab/revision/diff/universal+connection/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/universal+connection/3">v3</a>, <a href="https://ncatlab.org/nlab/show/universal+connection">current</a>

   also pointer to

   • Shrawan Kumar, A Remark on Universal Connections, Mathematische Annalen 260 (1982): 453-462 (dml:163680)

   diff, v3, current