Authors: Blagojević, Pavle 
Vrećica, Siniša
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Computational topology of equivariant maps from spheres to complements of arrangements
Journal: Transactions of the American Mathematical Society
Volume: 361
Issue: 2
First page: 1007
Last page: 1038
Issue Date: 1-Feb-2009
Rank: M21
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-08-04679-5
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 4-fan partition of 2-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.
Keywords: Equivariant obstruction theory | K-fans | Partition of measures
Publisher: American Mathematical Society
Project: Advanced methods for cryptology and information processing 

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