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nLab > Latest Changes: flavours of cobordism cohomology theories -- table

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1 to 17 of 17

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    a bare table, to be !include-ed under “Related entries” in pertinent entries

    Am trying to bring some order into the mess of entries of cobordism cohomology theories…

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    changed the title to disambiguate from the general floating TOC of cobordism theory

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 20th 2020

    Added Schwede’s mO and mU.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2020
    • (edited Nov 21st 2020)

    Okay. I have created a stub entry global equivariant bordism homology theory to make these links work.

    (I’d like to not leave broken links around too much, better to create a quick stub entry for them to point to. Besides making look their home entry broken and messy, broken links tend to mislead hapless users to click on them and inadvertently create broken entries, which we then have to clean up. Also, if nothing else, one usually has a reference at hand for the given keyword, so that one can just as well make a stub entry right away that will be of actual use, however small.)

    This list here I intended as a bare table of contents for easy overview of entries with further details; so that technical fine print such as the qualities of a given representing spectrum (or indeed the use of any spectrum in the first place) should better be relegated to the entries that are being listed here.

    In this vein I have edited your addition a little. For instance the item “ultracommutative ring spectrum” (a new stub entry) no longer appears listed here, but does appear in the entry behind the respective links.

    Okay?

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 21st 2020
    • (edited Nov 21st 2020)

    Thanks, Urs! The spectrum MO also has a global incarnation, by the way. Currently, the list seemingly indicates that mO is the only one that is global equivariant. (And vice versa, mO and mU can be restricted to a nonglobal equivariant spectrum.)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2020
    • (edited Nov 21st 2020)

    I was just reformatting the addition you made in rev 2. Maybe I misunderstood your intention?

    But in either case this is just the beginning of a list that can be much expanded. Let’s create more of the relevant entries and then add pointer to them to the list.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 23rd 2020

    added one more item to the list: MString

    (pointing to an old entry string bordism, which now redirects for MStringMString; as many of these entries it remains much underdeveloped)

    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 24th 2020

    Re #3: I was just trying to say that the current entry attaches the adjective “global” only to mO and mU, not to MO and MU.

    But all four have equal status with respect to globality: all four spectra can be defined as global equivariant spectra.

    So why should two of them be referred to as “global” and the other two not?

    Maybe mO and mU should be called global Thom spectra, and MO and MU global bordism spectra?

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 24th 2020
    • (edited Nov 24th 2020)

    Yes, and I was just trying to say that this was not my decision, but seemingly yours, in rev 2, which I only meant to format differently.

    But we agree that the table needs to be completed more properly. We’ll do it.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 3rd 2020

    added the item MFr and made that redirect to stable Cohomotopy for the time being (eventually this should be a separate entry).

    diff, v5, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 6th 2020

    added the item MUFr for Conner-Floyd’s (U,fr)(U,fr)-cobordism theory (UU-manifolds with FrFr-boundaries)

    diff, v6, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeDec 10th 2020

    am adding an item equivariant MFr (for equivariant framed bordism theory)

    diff, v7, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeDec 18th 2020

    am adding one more item to the list: MSUFr (for bordism theory of SU-manifolds with FrFr-boundaries, as on the last pages of Conner-Floyd 66)

    diff, v8, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2020
    • (edited Feb 18th 2021)

    am adding one more item to the list: MΩΩSU(n) – Ravenel’s X(n)X(n)

    diff, v9, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJan 11th 2021

    am adding one more item to the list: MOFr (i.e. unoriented bordism with framed boundary), to go along with MUFr and MSUFr

    diff, v13, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2021
    • (edited Feb 18th 2021)

    am adding one more item: MSpinc

    diff, v17, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeMar 16th 2023
    • (edited Mar 16th 2023)

    added the item MString

    [edit: sorry, never mind, the item was of course already there]

    diff, v19, current

1 to 17 of 17

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