The diffeomorphic types of the complements of arrangements in ??3 II |
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| Authors: | ShaoBo Wang and Stephen S-T Yau |
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| Institution: | (1) Strata Marketing, Inc, Chicago, IL 60603, USA;(2) Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA |
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| Abstract: | For any arrangement of hyperplanes in ℂℙ3, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the
arrangement of hyperplanes. In this paper, we give a sufficient combinatoric condition for two arrangements of hyperplanes
to be diffeomorphic to each other. In particular we have found sufficient conditions on combinatorics for the arrangement
of hyperplanes whose moduli space is connected. This generalizes our previous result on hyperplane point arrangements in ℂℙ3.
This work was partially supported by NSA grant and NSF grant |
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| Keywords: | arrangement of hyperplanes soul of arrangement combinational geometry of arrangement differential and topological structure of complement of arrangement |
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