### On the simple connectedness of hyperplane complements in dual polar spaces

Ilaria Cardinali, Bart De Bruyn UGent (2009) 309. p.294-303
abstract
Let \$\Delta\$ be a dual polar space of rank \geq 4\$, \$ be a hyperplane of \$\Delta\$ and \$\Gamma: = \Delta\setminus H\$ be the complement of \$ in \$\Delta\$. We shall prove that, if all lines of \$\Delta\$ have more than \$ points, then \$\Gamma\$ is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar spaces, arise from embeddings.
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
simple connectedness, universal embedding, hyperplanes, diagram geometry, dual polar spaces
journal title
Discrete Mathematics
Discrete Math.
volume
309
pages
294 - 303
Web of Science type
Article
Web of Science id
000262066400002
JCR category
MATHEMATICS
JCR impact factor
0.548 (2009)
JCR rank
158/251 (2009)
JCR quartile
3 (2009)
ISSN
0012-365X
DOI
10.1016/j.disc.2007.12.006
language
English
UGent publication?
yes
classification
A1
I don't know the status of the copyright for this publication
id
879048
handle
http://hdl.handle.net/1854/LU-879048
date created
2010-02-24 13:58:05
date last changed
2010-03-05 08:59:22
```@article{879048,
abstract     = {Let \\${\textbackslash}Delta\\$ be a dual polar space of rank  {\textbackslash}geq 4\\$, \\$ be a hyperplane of \\${\textbackslash}Delta\\$
and \\${\textbackslash}Gamma: = {\textbackslash}Delta{\textbackslash}setminus H\\$ be the complement of \\$ in \\${\textbackslash}Delta\\$. We shall prove that, if all lines of \\${\textbackslash}Delta\\$ have more than \\$ points, then \\${\textbackslash}Gamma\\$ is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar spaces, arise from embeddings.},
author       = {Cardinali, Ilaria and De Bruyn, Bart and Pasini, Antonio},
issn         = {0012-365X},
journal      = {Discrete Mathematics},
keyword      = {simple connectedness,universal embedding,hyperplanes,diagram geometry,dual polar spaces},
language     = {eng},
pages        = {294--303},
title        = {On the simple connectedness of hyperplane complements in dual polar spaces},
url          = {http://dx.doi.org/10.1016/j.disc.2007.12.006},
volume       = {309},
year         = {2009},
}

```
Chicago
Cardinali, Ilaria, Bart De Bruyn, and Antonio Pasini. 2009. “On the Simple Connectedness of Hyperplane Complements in Dual Polar Spaces.” Discrete Mathematics 309: 294–303.
APA
Cardinali, I., De Bruyn, B., & Pasini, A. (2009). On the simple connectedness of hyperplane complements in dual polar spaces. Discrete Mathematics, 309, 294–303.
Vancouver
1.
Cardinali I, De Bruyn B, Pasini A. On the simple connectedness of hyperplane complements in dual polar spaces. Discrete Mathematics. 2009;309:294–303.
MLA
Cardinali, Ilaria, Bart De Bruyn, and Antonio Pasini. “On the Simple Connectedness of Hyperplane Complements in Dual Polar Spaces.” Discrete Mathematics 309 (2009): 294–303. Print.