Abstract
We prove that the complement of any affine 2-arrangement in Rd is minimal, that is, it is homotopy equivalent to a cell complex with as many i-cells as its ith rational Betti number. For the proof, we provide a Lefschetz-type hyperplane theorem for complements of 2-arrangements, and introduce Alexander duality for combinatorialMorse functions. Our results greatly generalize previous work by Falk, Dimca-Papadima, Hattori, Randell and Salvetti-Settepanella and others, and they demonstrate that in contrast to previous investigations, a purely combinatorial approach suffices to show minimality and the Lefschetz Hyperplane Theorem for complements of complex hyperplane arrangements.
Original language | English |
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Article number | jtu018 |
Pages (from-to) | 1200-1220 |
Number of pages | 21 |
Journal | Journal of Topology |
Volume | 7 |
Issue number | 4 |
DOIs | |
State | Published - 21 Jan 2013 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Geometry and Topology