The lecture focuses on how much topological information about an
arrangement of hyperplanes is contained in the intersection lattice (i.e.
the combinatorics). Rybnikov found two line arrangements with isomorphic
combinatorics but non-isomorphic fundamental groups. Here, complete proofs
of
Rybnikov's statements are provided. Then it is shown how to find two real
line arrangements that have isomorphic combinatorics, but their
complexifications have non-homeomorphic embeddings in the projective
plane.

Keywords:

Hyperplane Arrangements; Line Arrangements; Combinatorics.

Lecture #10702

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