The diffeomorphic types of the complements of arrangements in ℂℙ3 II |
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Authors: | ShaoBo Wang 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 ??3, 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 ??3. |
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