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<h1>Kai-Uwe Bux</h1>
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<th width="20%"><a href="pg_e01.html">Home</a></th>
<th width="20%" bgcolor="yellow">Research</th>
<th width="20%"><a href="pg_e03.html">Teaching</a></th>
<th width="20%"><a href="pg_e04.html">Publications</a></th>
<th width="20%"><a href="pg_e05.html">Projects</a></th>
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<h2>Interests</h2>
<p>
I am engaged in algebra and geometry---especially in geometric
group theory, buildings and other CAT(0) spaces,
arithmetic groups.
More recently,
I have become interested in Morse theory on cell complexes in the spirit
of M. Bestvina and
N. Brady [Invent. Math. 129 (1997) p. 445 - 470].
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<p>
Soluble groups are the main object of my research. As a student
of Robert Bieri's, I search for ways to compute the
so called Bieri-Neumann-Strebel-Renz invariants of these groups.
Here, the main tool is to consider complexes on which the
groups act nicely, and
the main difficulty is to get topological information about
the complexes by means of their geometric or combinatorial
structure. I try to find techniques to do this.
</p>
<p>
In terms of methods, I become more and more interested in Morse theory
on cell complexes which, from my point of view, is a way to turn
local information about links into global information about
connectivity of complexes or large subcomplexes.
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<h2>Summary of research</h2>
<p>
I have studied mainly finiteness properties of soluble
arithmetic groups and tried to compute their
Bieri-Neumann-Strebel-Renz invariants.
The main tool was to consider actions of these groups on associated
Bruhat-Tits buildings.
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<p>
I have been also doing research on Morse theory on cell complexes
which I plan to pay even more attention to in the future.
Part of my present view of this subject is explained in the
joint paper of C. Gonzales and myself.
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<p><a href="pg_e04.math.html">Mathematical (pr)e-prints</a></p>
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