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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2010
    • (edited Dec 21st 2010)

    I finally learned about the general abstract story behind the notion of orientation in RR-cohomology, for RR an E E_\infty-ring, in terms of trivialization of GL 1(R)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.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeDec 21st 2010

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

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 27th 2016
    • (edited May 27th 2016)

    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 EE-orientation for vector bundles with GG-structure is equivalently the class of a ring spectrum homomorphism MGEM G \longrightarrow E.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 10th 2019

    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