The aim of this lecture is to describe the natural map from the homology
to the locally finite homology of an arrangement complement with
coefficients in a generic resonant rank one local system. If the local system is
non-resonant then this map is an isomorphism, but in general this is not
true. For a real complexified arrangement the bounded chambers of the real
arrangement touching no resonant edges only generate the image of the map,
but do not form a basis. For a fiber type arrangement is constructed a
finite chain complex model for the complex of locally finite chains of the
universal cover of the complement. This model can be used to determine
the relations among the bounded chambers.

Keywords:

Hyperplane Arrangements

Lecture #10706

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