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nLab > Latest Changes: HNN-extension

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeApr 3rd 2012

    I have created a stub HNN-extension. I have been wondering how to link in the connection between homotopy colimits and graphs of groups (see Fiore, Luck and Sauer), any ideas? Perhpas it will have to wait until there is a graphs of groups and a complexes of groups entry

  2. I have added a 2-categorical description of the HNN-extension. See https://mathoverflow.net/q/352894/117693 for a discussion (Should the MO post be referenced?) Sorry if I made anything wrong, this is my first submission.

    Lukas Heger

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorLukas Heger
    • CommentTimeDec 10th 2022
    One could even consider adding this example to the entry inserter.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2022

    regarding the original edit in #1, I have now:

    • fixed wording and typesetting of the definition,

    • added the actual original references

    • added an Idea-section

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2022
    • (edited Dec 11th 2022)

    Regarding the edit from #2:

    I have made some substantial edits to the new section “As a 2-colimit” (here) in order to bring out more carefully (maybe: pedantically, but this is important) the fact that the delooping groupoid-construction

    B(−):Grps→Grpds \mathbf{B}(-) \;\colon\; Grps \to Grpds

    is not fully-faithful (only regarded as landing in pointed objects among groupoids does it become a full embedding).

    Of course this is essentially the point that makes the intended construction in this section work in the first place, but it still important to make the notational distinction.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2022

    also, I have now tried to harmonize (and fix) the notation: Now, throughout, the ambient group is denoted “GG” and the given subgroup “HH”, as usual.

    But maybe double-check that I didn’t miss some occurrence.

    diff, v4, current

1 to 6 of 6

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