On the number of connected components in complements to arrangements of submanifolds

I. N. Shnurnikov

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arXiv · 1209.3476

On the number of connected components in complements to arrangements of submanifolds

I. N. Shnurnikov

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Abstract

We consider arrangements of n connected codimensional one submanifolds in closed d-dimensional manifold M. Let f be the number of connected components of the complement in M to the union of submanifolds. We prove the sharp lower bound for f via n and homology group H_{d-1}(M). The sets of all possible f-values for given n are studied for hyperplane arrangements in real projective spaces and for subtori arrangements in d-dimensional tori.

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I. N. Shnurnikov. 2012-09-16. On the number of connected components in complements to arrangements of submanifolds. https://arxiv.org/abs/1209.3476

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