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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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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
   • CommentTimeSep 24th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded these pointers: * [[Victor Buchstaber]], _The Chern–Dold character in cobordisms. I_, Russian original: Mat. Sb. (N.S.), 1970 Volume 83(125), Number 4(12), Pages 575–595 ([mathnet:3530](http://m.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=3530&option_lang=eng)) English translation: Mathematics of the USSR-Sbornik, Volume 12, Number 4, AMS 1970 ([doi:10.1070/SM1970v012n04ABEH000939](https://iopscience.iop.org/article/10.1070/SM1970v012n04ABEH000939)) * [[Victor Buchstaber]], A. P. Veselov, _Chern-Dold character in complex cobordisms and abelian varieties_ ([arXiv:2007.05782](https://arxiv.org/abs/2007.05782)) <a href="https://ncatlab.org/nlab/revision/diff/MU/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/12">v12</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   added these pointers:

   • Victor Buchstaber, The Chern–Dold character in cobordisms. I,

     Russian original: Mat. Sb. (N.S.), 1970 Volume 83(125), Number 4(12), Pages 575–595 (mathnet:3530)

     English translation: Mathematics of the USSR-Sbornik, Volume 12, Number 4, AMS 1970 (doi:10.1070/SM1970v012n04ABEH000939)

   • Victor Buchstaber, A. P. Veselov, Chern-Dold character in complex cobordisms and abelian varieties (arXiv:2007.05782)

   diff, v12, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 3rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Dai Tamaki]], [[Akira Kono]], Section 3.7 in: _Generalized Cohomology_, Translations of Mathematical Monographs, American Mathematical Society, 2006 ([ISBN: 978-0-8218-3514-2](https://bookstore.ams.org/mmono-230)) <a href="https://ncatlab.org/nlab/revision/diff/MU/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/24">v24</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   added pointer to:

   • Dai Tamaki, Akira Kono, Section 3.7 in: Generalized Cohomology, Translations of Mathematical Monographs, American Mathematical Society, 2006 (ISBN: 978-0-8218-3514-2)

   diff, v24, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 11th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Stanley Kochman]], Section 4.4 of: _[[Bordism, Stable Homotopy and Adams Spectral Sequences]]_, Fields Institute Monographs, American Mathematical Society, 1996 ([cds:2264210](https://cdsweb.cern.ch/record/2264210)) <a href="https://ncatlab.org/nlab/revision/diff/MU/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/26">v26</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   added pointer to:

   • Stanley Kochman, Section 4.4 of: Bordism, Stable Homotopy and Adams Spectral Sequences, Fields Institute Monographs, American Mathematical Society, 1996 (cds:2264210)

   diff, v26, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 11th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Robert Stong]], Chapter VII of: _Notes on Cobordism theory_, Princeton University Press, 1968 ([toc pdf](http://pi.math.virginia.edu/StongConf/Stongbookcontents.pdf), [ISBN:9780691649016](http://press.princeton.edu/titles/6465.html)) <a href="https://ncatlab.org/nlab/revision/diff/MU/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/26">v26</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   added pointer to:

   • Robert Stong, Chapter VII of: Notes on Cobordism theory, Princeton University Press, 1968 (toc pdf, ISBN:9780691649016)

   diff, v26, current

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJan 11th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded a section about MU-cohomology groups. <a href="https://ncatlab.org/nlab/revision/diff/MU/29">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/29">v29</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   Added a section about MU-cohomology groups.

   diff, v29, current

6. • CommentRowNumber6.
   • CommentAuthorDoronGrossmanNaples
   • CommentTimeOct 19th 2022
   • PermaLink
   Author: DoronGrossmanNaples
   Format: MarkdownItexAs noted in the article on complex orientable cohomology theories, complex orientations do not correspond to maps of E-infinity rings, just homotopy-commutative rings. Hopkins and Lawson (https://arxiv.org/abs/1603.00047) have given conditions under which this map can be made E-infinity, but that's a more complicated story. <a href="https://ncatlab.org/nlab/revision/diff/MU/33">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/33">v33</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   As noted in the article on complex orientable cohomology theories, complex orientations do not correspond to maps of E-infinity rings, just homotopy-commutative rings. Hopkins and Lawson (https://arxiv.org/abs/1603.00047) have given conditions under which this map can be made E-infinity, but that’s a more complicated story.

   diff, v33, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Ulrich Bunke]], [[Thomas Schick]], [[Ingo Schroeder]], [[Moritz Wiethaup]], *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; <a href="https://ncatlab.org/nlab/revision/diff/MU/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/MU/37">v37</a>, <a href="https://ncatlab.org/nlab/show/MU">current</a>

   added pointer to:

   • Ulrich Bunke, Thomas Schick, Ingo Schroeder, Moritz Wiethaup, 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]

   diff, v37, current