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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
   • CommentTimeJun 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Georges de Rham]], Chapter III of: *Differentiable Manifolds -- Forms, Currents, Harmonic Forms*, Grundlehren **266**, Springer (1984) &lbrack;[doi:10.1007/978-3-642-61752-2](https://doi.org/10.1007/978-3-642-61752-2)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/current+%28distribution+theory%29/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/current+%28distribution+theory%29/2">v2</a>, <a href="https://ncatlab.org/nlab/show/current+%28distribution+theory%29">current</a>

   added pointer to:

   • Georges de Rham, Chapter III of: Differentiable Manifolds – Forms, Currents, Harmonic Forms, Grundlehren 266, Springer (1984) [doi:10.1007/978-3-642-61752-2]

   diff, v2, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 10th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added proper publication data to the references that were listed here <a href="https://ncatlab.org/nlab/revision/diff/current+%28distribution+theory%29/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/current+%28distribution+theory%29/3">v3</a>, <a href="https://ncatlab.org/nlab/show/current+%28distribution+theory%29">current</a>

   I have added proper publication data to the references that were listed here

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 10th 2023
   • (edited Jun 10th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a section "References -- Applications", in order to have a place to record this content: *** Currents appear as part of "geometric cycles" for [[differential cobordism cohomology]] by actual [[cobordism]]-classes equipped with [[differential geometry|differential geometric]] data: * [[Ulrich Bunke]], [[Thomas Schick]], Ingo Schroeder, Moritz Wiethaup, §4.1.4 in: *Landweber exact formal group laws and smooth cohomology theories*, Algebr. Geom. Topol. **9** (2009) 1751-1790 &lbrack;[arXiv:0711.1134](https://arxiv.org/abs/0711.1134), [doi:10.2140/agt.2009.9.1751](https://doi.org/10.2140/agt.2009.9.1751)&rbrack; and in the [[Hodge-filtered differential cohomology|Hodge-filtered]] version: * {#Haus22} [[Knut Bjarte Haus]], §2.3, §4.12 in: *Geometric Hodge filtered complex cobordism*, PhD thesis (2022) &lbrack;[ntnuopen:3017489](https://ntnuopen.ntnu.no/ntnu-xmlui/handle/11250/3017489)&rbrack; * {#HausQuick22} [[Knut Bjarte Haus]], [[Gereon Quick]], §2 of: *Geometric Hodge filtered complex cobordism* &lbrack;[arXiv:2210.13259](https://arxiv.org/abs/2210.13259)&rbrack; *** <a href="https://ncatlab.org/nlab/revision/diff/current+%28distribution+theory%29/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/current+%28distribution+theory%29/3">v3</a>, <a href="https://ncatlab.org/nlab/show/current+%28distribution+theory%29">current</a>

   added a section “References – Applications”, in order to have a place to record this content:

   ---

   Currents appear as part of “geometric cycles” for differential cobordism cohomology by actual cobordism-classes equipped with differential geometric data:

   • Ulrich Bunke, Thomas Schick, Ingo Schroeder, Moritz Wiethaup, §4.1.4 in: Landweber exact formal group laws and smooth cohomology theories, Algebr. Geom. Topol. 9 (2009) 1751-1790 [arXiv:0711.1134, doi:10.2140/agt.2009.9.1751]

   and in the Hodge-filtered version:

   • {#Haus22} Knut Bjarte Haus, §2.3, §4.12 in: Geometric Hodge filtered complex cobordism, PhD thesis (2022) [ntnuopen:3017489]

   • {#HausQuick22} Knut Bjarte Haus, Gereon Quick, §2 of: Geometric Hodge filtered complex cobordism [arXiv:2210.13259]

   ---

   diff, v3, current