TY - CHAP
T1 - Combinatorial stratifications and minimality of two-arrangements
AU - Adiprasito, Karim A.
N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85028619866&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-319-20155-9_3
DO - https://doi.org/10.1007/978-3-319-20155-9_3
M3 - فصل
T3 - Springer INdAM Series
SP - 11
EP - 14
BT - Springer INdAM Series
ER -