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Regions Cut by Arrangements of Topological Spheres

Published online by Cambridge University Press:  20 November 2018

Lewis Pakula*
Affiliation:
Department of Mathematics University of Rhode Island Kingston, Rhode Island 02881 U.S.A.
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Abstract

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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.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Anusiak, J., On set theoretically independent collections of balls, Colloquium Math. XIII, Fasc. 2(1965), 223233.Google Scholar
2. Griinbaum, B., Arrangements and Spreads, CBMS Regional Conference Series in Math. (10), American Math. Soc, (1972), Providence, RI.Google Scholar
3. Munkres, J., Elements of Algebraic Topology, Addison-Wesley, Reading, MA, 1984.Google Scholar
4. Pakula, L. and Schwartzman, S., Independence for sets of topological spheres, Canadian Math. Bull. (4) 34(1991), 520524.Google Scholar
5. Spanier, E., Algebraic Topology, McGraw-Hill, New York, 1966.Google Scholar
6. Winder, R. O., Partitions of N-space by hyperplanes, SIof, A. J. Applied Math. 14(1966), 811818.Google Scholar
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. Zaslavsky, T., A combinatorial analysis of topological dissections, Advances in Math. 25(1977), 267285.Google Scholar
9. Zaslavsky, T., Extremal arrangements of hyperplanes.In: Discrete Geometry and Convexity, Ann. New York Acad. Sci. 440(1985), 6987.Google Scholar