4
$\begingroup$

In one of the talks of J.P. May he mentioned some examples of structure groups and their classification spaces (he mentioned: O, U, SO, SU, Sp, Spin, String, Top, STop, F and SF). Most of them are familiar with me, but I never heard of the structure group String. Googling isn't helping much, because you always find yourself reading some physics article. The question is simple:

  • What does the group $String$ mean in the context of fibre bundles?
  • In what articles / books are they explained ?
  • 0
    Related: http://math.stackexchange.com/q/46306/152. But there is a problem here: String is *not* a Lie group.2011-11-23
  • 0
    Some explanations: http://golem.ph.utexas.edu/category/2008/10/string_and_fivebranestructures.html (and links there)2011-11-23
  • 0
    Thanks for your answers. It is really useful. To be complete, the new article http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.2131v1.pdf (also obtainable from the golem site gives some deeper insites. I have also read about a FiveBrane structure groups, whicht sits in $\ldots \leftarrow Spin(n) \leftarrow String(n) \leftarrow FiveBrane(n)$. I don't know about groups beyond FiveBrane(n), but probably this sequence can be added indefinetly, if meaningful. Probably the neme FiveBrane stems from connections with Brane Theory. so in retrospect, I wonder what is beyond that...2011-11-24
  • 0
    To answer my own question (not really a proof, but a mere observation): Looking at http://ncatlab.org/nlab/show/Fivebrane+group and the celebrated Bott-periodicity, I think there is nothing beyond the FiveBrane(n) group, but please do correct me.2011-11-24
  • 0
    Why, there is an infinite Postnikov tower (FiveBrane is a 7-connected cover but there is a 8-connected cover and so on).2011-11-25

1 Answers 1

2

You could try the nLab page

  • 0
    Thanks for your usefuk remark. I shall put nLab in my favorites.2011-11-24