groups, which will be our basic tool for the construction of lattices, are introduced in Chapter \[ch:complexes\_of\_groups\].

The last three chapters form the part of the thesis where we discuss our results. In Chapter \[ch:wagoner\], we construct Wagoner complexes associated to groups of Kac-Moody type. In Chapter \[ch:stability\], we prove homological stability for large classes of classical groups. Finally, in Chapter \[ch:lattices\], we construct new lattices in two-dimensional affine buildings and calculate their homology.

Chapter \[ch:problems\] lists open problems related to the results of this thesis. It may serve as the starting point for further research in this direction.

Main results {#ch:results}
============

We begin this thesis with a high-level overview of the main results, which are contained in Chapters \[ch:wagoner\], \[ch:stability\] and \[ch:lattices\]. Readers that are unfamiliar with the terminology should consult Figure \[fig:leitfaden\] on page to find the location of the prerequisites or start directly with Chapter \[ch:basic\] and come back for this overview at a later point.

Wagoner complexes {#sec:wagoner_results}
-----------------

Wagoner complexes are certain simplicial complexes first constructed by Wagoner in [@Wag:BSK:73]. In his original construction, they were associated to the group $\operatorname{GL}_n(R)$ over an arbitrary ring $R$. Wagoner used the homotopy groups of these complexes 