8,609 research outputs found
Constructing Buildings and Harmonic Maps
In a continuation of our previous work, we outline a theory which should lead
to the construction of a universal pre-building and versal building with a
-harmonic map from a Riemann surface, in the case of two-dimensional
buildings for the group . This will provide a generalization of the space
of leaves of the foliation defined by a quadratic differential in the classical
theory for . Our conjectural construction would determine the exponents
for WKB problems, and it can be put into practice on examples.Comment: 61 pages, 24 figures. Comments are welcom
Intersection problem for Droms RAAGs
We solve the subgroup intersection problem (SIP) for any RAAG G of Droms type
(i.e., with defining graph not containing induced squares or paths of length
3): there is an algorithm which, given finite sets of generators for two
subgroups H,K of G, decides whether is finitely generated or not,
and, in the affirmative case, it computes a set of generators for .
Taking advantage of the recursive characterization of Droms groups, the proof
consists in separately showing that the solvability of SIP passes through free
products, and through direct products with free-abelian groups. We note that
most of RAAGs are not Howson, and many (e.g. F_2 x F_2) even have unsolvable
SIP.Comment: 33 pages, 12 figures (revised following the referee's suggestions
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