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Quomodocumque on F_un (Update 10-21)

Posted By __Thas__ On October 14, 2008 @ 2:04 pm In __news__ | __No Comments__

Quomodocumque has an interesting post on F_un, buildings, the braid group and ^{[1]}, starting from the Kapranov-Smirnov observation that should be considered as the braid group on n-strings (see also this post ^{[2]}).

So then, what is ? For it turns out that one can use Serre’s-tree results in the description of to postulate that

, the amalgamated free product of two copies over over the common subgroup .

For higher the work of Lisa Carbone ^{[3]} suggest the following answer :

“ is something like the mapping class group of a disc with n boundary components instead of n punctures.”

**UPDATE tuesday october 20th**

In a follow-up post, F_un and the braid group – a note of skepticism ^{[4]}, arguments are collected **against** the claim that the d-string braid group should be . One of the arguments being that is a subgroup of whereas cannot be embedded into .

Article printed from F_un mathematics: **http://cage.ugent.be/~kthas/Fun**

URL to article: **http://cage.ugent.be/~kthas/Fun/index.php/quomodocumque-on-f_un.html**

URLs in this post:

[1] Image: **http://quomodocumque.wordpress.com/2008/10/13/f_1-buildings-the-braid-group-gl_nf_1t1t/**

[2] this post: **http://cage.ugent.be/~kthas/Fun/index.php/f_un-and-braid-groups.html**

[3] Lisa Carbone: **http://www.math.rutgers.edu/~carbonel/**

[4] F_un and the braid group – a note of skepticism: **http://quomodocumque.wordpress.com/2008/10/20/f_1-and-the-braid-group-a-note-of-skepticism/**

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