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On panel-regular ~A_2 lattices. (arXiv:1608.07141v2 [math.GR] UPDATED)
来源于:arXiv
We study lattices on ~A_2 buildings that preserve types, act regularly on
each type of edge, and whose vertex stabilizers are cyclic. We show that
several of their properties, such as their automorphism group and isomorphism
class, can be determined from purely combinatorial data. As a consequence we
can show that the number of such lattices (up to isomorphism) grows
super-exponentially with the thickness parameter q.
We look in more detail at the 3295 lattices with q in {2,3,4,5}. We show that
with one exception for each q these are all exotic. For the exotic examples we
prove that the automorphism group of the lattice and of the building coincide,
and that two lattices are quasi-isometric only if they are isomorphic. 查看全文>>