|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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