Combinatorial stratifications and minimality of two-arrangements

Karim A. Adiprasito

doi:10.1007/978-3-319-20155-9_3

Combinatorial stratifications and minimality of two-arrangements

Karim A. Adiprasito^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

I present a result according to which the complement of any affine 2-arrangement in ℝ^d 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 language	English
Title of host publication	Springer INdAM Series
Publisher	Springer International Publishing
Pages	11-14
Number of pages	4
DOIs	https://doi.org/10.1007/978-3-319-20155-9_3
State	Published - 2015

Publication series

Name	Springer INdAM Series
Volume	12
ISSN (Print)	2281-518X
ISSN (Electronic)	2281-5198

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Publisher Copyright:
© Springer International Publishing Switzerland 2015.

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10.1007/978-3-319-20155-9_3

Cite this

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Combinatorial stratifications and minimality of two-arrangements

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