Combinatorial stratifications and minimality of two-arrangements

Karim A. Adiprasito*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


I present a result according to which 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 Betti number. To this end, we prove that the Björner–Ziegler complement complexes, induced by combinatorial stratifications of any essential 2-arrangement, admit perfect discrete Morse functions. This result extend previous work by Falk, Dimca–Papadima, Hattori, Randell, and Salvetti–Settepanella, among others.

Original languageAmerican English
Title of host publicationSpringer INdAM Series
PublisherSpringer International Publishing
Number of pages4
StatePublished - 2015

Publication series

NameSpringer INdAM Series
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.


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