Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2016

    Finally I am starting an entry Platonic 2-group.

    For the moment, all it has is the statement of Epa-Ganter 16, prop. 4.1, rephrased as the diagram

    𝒢 uni[i] BG ADE B 3/|G ADE| String(SU(2)) BSU(2) c 2 B 3U(1) \array{ \mathcal{G}_{uni}[i] &\longrightarrow& \mathbf{B}G_{ADE} &\longrightarrow& \mathbf{B}^3 \mathbb{Z}/{\vert G_{ADE}\vert} \\ \downarrow && \downarrow && \downarrow \\ String(SU(2)) &\longrightarrow& \mathbf{B} SU(2) &\underset{\mathbf{c}_2}{\longrightarrow}& \mathbf{B}^3 U(1) }
    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 25th 2016

    I added a comment on what the ii in your diagram means.

    It’s reminiscent of my quest to find a basic 2-group for Klein 2-geometry. I was looking for copies of some group sitting on the vertices of a cube, and then wondering about symmetries.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2016

    I added a comment on what the ii in your diagram means.

    Thanks! I also added that to the diagram, and harmonized the notation a little.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 8th 2018

    Idle thought in passing: can these Platonic 2-groups be lifted to the fivebrane 6-group?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2018

    It sure looks like the pattern wants to continue. But since the Platonic n-groups are, crucially, not just the pullbacks of the Whitehead stages, it is not evident if it will work.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)