The fundamental group of the complement of an arrangement of complex hyperplanes
β Scribed by William A. Arvola
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 535 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0040-9383
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π SIMILAR VOLUMES
We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range,
## Every arrangement %' of a&e hyperplanes in Rd determines a partition of Rd into open topological cells. The face lattice L(X) of this partition was the object of a smdy by Barnabei and Brini, wko de.;ermined the homotopy type of its intervals. We use g:am&ic con~huctions from the theory of conv
We consider the class P n of labeled posets on n elements which avoid certain three-element induced subposets. We show that the number of posets in P n is (n+1) n&1 by exploiting a bijection between P n and the set of regions of the arrangement of hyperplanes in R n of the form x i &x j =0 or 1 for