On Complexes of Products and Products of Complexes

This thesis addresses the various subdivisions of Bergman complexes of matroids. It investigates the relation of those subdivisions with decomposition formulas for supporting matroid types. It shows that for lattice path matroids Bergman complexes are easy to describe. The second part introduces decomposition complexes, which are common generalizations of order complexes, nested set complexes and Bergman complexes definable for all posets and even acyclic categories.