Geodesic
Regions Cut by Arrangements of Topological Spheres
Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 241-244

Voir la notice de l'article provenant de la source Cambridge University Press

We define an arrangement of pseudohyperplanes as an image of a topological sphere arrangement with appropriate intersections, and prove that the complement components are then homologically trivial. We apply this to extend a formula of Winder and Zaslavsky.
DOI : 10.4153/CMB-1993-034-5
Mots-clés : 52B30, 51M20, 05A99 
Pakula, Lewis. Regions Cut by Arrangements of Topological Spheres. Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 241-244. doi: 10.4153/CMB-1993-034-5
@article{10_4153_CMB_1993_034_5,
     author = {Pakula, Lewis},
     title = {Regions {Cut} by {Arrangements} of {Topological} {Spheres}},
     journal = {Canadian mathematical bulletin},
     pages = {241--244},
     year = {1993},
     volume = {36},
     number = {2},
     doi = {10.4153/CMB-1993-034-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-034-5/}
}
TY  - JOUR
AU  - Pakula, Lewis
TI  - Regions Cut by Arrangements of Topological Spheres
JO  - Canadian mathematical bulletin
PY  - 1993
SP  - 241
EP  - 244
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-034-5/
DO  - 10.4153/CMB-1993-034-5
ID  - 10_4153_CMB_1993_034_5
ER  - 
%0 Journal Article
%A Pakula, Lewis
%T Regions Cut by Arrangements of Topological Spheres
%J Canadian mathematical bulletin
%D 1993
%P 241-244
%V 36
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-034-5/
%R 10.4153/CMB-1993-034-5
%F 10_4153_CMB_1993_034_5

[1] 1. Anusiak, J., On set theoretically independent collections of balls, Colloquium Math. XIII, Fasc. 2(1965), 223–233. Google Scholar

[2] 2. Griinbaum, B., Arrangements and Spreads, CBMS Regional Conference Series in Math. (10), American Math. Soc, (1972), Providence, RI. Google Scholar

[3] 3. Munkres, J., Elements of Algebraic Topology, Addison-Wesley, Reading, MA, 1984. Google Scholar

[4] 4. Pakula, L. and Schwartzman, S., Independence for sets of topological spheres, Canadian Math. Bull. (4) 34(1991), 520–524. Google Scholar

[5] 5. Spanier, E., Algebraic Topology, McGraw-Hill, New York, 1966. Google Scholar

[6] 6. Winder, R. O., Partitions of N-space by hyperplanes, SIof, A. J. Applied Math. 14(1966), 811–818. Google Scholar

[7] 7. Zaslavsky, T., Facing up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes, Memoirs American Math. Soc. (154), (1) 1(1975). Google Scholar

[8] 8. Zaslavsky, T., A combinatorial analysis of topological dissections, Advances in Math. 25(1977), 267–285. Google Scholar

[9] 9. Zaslavsky, T., Extremal arrangements of hyperplanes.In: Discrete Geometry and Convexity, Ann. New York Acad. Sci. 440(1985), 69–87. Google Scholar

Cité par Sources :