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ISSN 1088-6850(e) ISSN 0002-9947(p)

Computational topology of equivariant maps from spheres to complements of arrangements

Author(s): Pavle V. M. Blagojevic; Sinisa T. Vrecica; Rade T. Zivaljevic
Journal: Trans. Amer. Math. Soc. 361 (2009), 1007-1038.
MSC (2000): Primary 52A37, 55S35; Secondary 55M35
Posted: August 19, 2008
MathSciNet review: 2452832
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The problem of the existence of an equivariant map is a classical topological problem ubiquitous in topology and its applications. Many problems in discrete geometry and combinatorics have been reduced to such a question and many of them resolved by the use of equivariant obstruction theory. A variety of concrete techniques for evaluating equivariant obstruction classes are introduced, discussed and illustrated by explicit calculations. The emphasis is on $D_{2n}$ -equivariant maps from spheres to complements of arrangements, motivated by the problem of finding a -fan partition of -spherical measures, where $D_{2n}$ is the dihedral group. One of the technical highlights is the determination of the $D_{2n}$ -module structure of the homology of the complement of the appropriate subspace arrangement, based on the geometric interpretation for the generators of the homology groups of arrangements.

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