Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric generators for braid-like groups   We study the problem of finding generators for the fundamental group G of a
space of the following sort: one removes a family of complex hyperplanes from n
dimensional complex vector space, or n dimensional complex hyperbolic space, or
the Hermitian symmetric space for O(2,n), and then takes the quotient by a
discrete group $P{\Gamma}$. The classical example is the braid group, but there
are many similar "braid-like" groups that arise in topology and algebraic
geometry. Our main result is that if $P{\Gamma}$ contains reflections in the
hyperplanes nearest the basepoint, and these reflections satisfy a certain
property, then G is generated by the analogues of the generators of the
classical braid group. We apply this to obtain generators for G in a particular
intricate example in complex hyperbolic space of dimension 13. The interest in
this example comes from a conjectured relationship between this braid-like
group and the monster simple group M, that gives geometric meaning to the
generators and relations in the Conway-Simons presentation of $(M \times M):2$.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int