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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 21st 2010
   • (edited Dec 21st 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI finally learned about the general abstract story behind the notion of orientation in $R$-cohomology, for $R$ an $E_\infty$-ring, in terms of trivialization of $GL_1(R)$-associated $\infty$-bundles -- from <a href="http://math.mit.edu/conferences/talbot/2007/tmfproc/Chapter14/MikesTalk3.pdf">this</a> lecture by Mike Hopkins I added some remark about that to [[orientation in generalized cohomology]]. Needs more polishing and expansion, but I have to interrupt for the moment.

   I finally learned about the general abstract story behind the notion of orientation in $R$-cohomology, for $R$ an $E_\infty$-ring, in terms of trivialization of $GL_1(R)$-associated $\infty$-bundles – from this lecture by Mike Hopkins

   I added some remark about that to orientation in generalized cohomology. Needs more polishing and expansion, but I have to interrupt for the moment.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeDec 21st 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAnother discussion of orientation is also in Stong's notes :)

   Another discussion of orientation is also in Stong’s notes :)

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 27th 2016
   • (edited May 27th 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to _[[orientation in generalized cohomology]]_ a section with the traditional definition ([here](https://ncatlab.org/nlab/show/orientation+in+generalized+cohomology#TraditionalDefinition)). It includes statement and proof ([here](https://ncatlab.org/nlab/show/orientation+in+generalized+cohomology#UniversalEOrientationsAreEquivalentlyMorphismsOfRingSpectra)) that traditonally defined universal multiplicative $E$-orientation for vector bundles with $G$-structure is equivalently the class of a ring spectrum homomorphism $M G \longrightarrow E$.

   I have added to orientation in generalized cohomology a section with the traditional definition (here). It includes statement and proof (here) that traditonally defined universal multiplicative $E$-orientation for vector bundles with $G$-structure is equivalently the class of a ring spectrum homomorphism $M G \longrightarrow E$.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 10th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a rather unusual reference * Mattia Coloma, [[Domenico Fiorenza]], Eugenio Landi, _An exposition of the topological half of the Grothendieck-Hirzebruch-Riemann-Roch theorem in the fancy language of spectra_, ([arXiv:1911.12035](https://arxiv.org/abs/1911.12035)) with Latin section titles. <a href="https://ncatlab.org/nlab/revision/diff/orientation+in+generalized+cohomology/52">diff</a>, <a href="https://ncatlab.org/nlab/revision/orientation+in+generalized+cohomology/52">v52</a>, <a href="https://ncatlab.org/nlab/show/orientation+in+generalized+cohomology">current</a>

   Added a rather unusual reference

   • Mattia Coloma, Domenico Fiorenza, Eugenio Landi, An exposition of the topological half of the Grothendieck-Hirzebruch-Riemann-Roch theorem in the fancy language of spectra, (arXiv:1911.12035)

   with Latin section titles.

   diff, v52, current