Incidence Theorems on manifolds

by JŸrgen_Richter-Gebert

The talk focuses on the interplay of geometric incidence theorems,
algebraic structures and  cycle structures on manifolds.
It will we shown how the combinatorics of many proofs for
incidence theorems can be considered as directly related to a
cycle structure on triangulated manifolds. This relation, which
interprets algebraic cancellation patterns in a topological
way, can be used on the one hand to analyze incidence
theorems in order to find an easy proof of the theorem. On the other hand it can
be used to generate incidence theorems in a systematic way.
Relations to oriented matroid theory and and the theory of
polygonal tilings will be outlined during the talk.