Combinatorial stratifications and minimality of 2-arrangements

Karim A. Adiprasito*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageAmerican English
Article numberjtu018
Pages (from-to)1200-1220
Number of pages21
JournalJournal of Topology
Volume7
Issue number4
DOIs
StatePublished - 21 Jan 2013
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 London Mathematical Society.

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