Computational topology of equivariant maps from spheres to complements of arrangements
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- by Pavle V. M. Blagojević, Siniša T. Vrećica and Rade T. Živaljević PDF
- Trans. Amer. Math. Soc. 361 (2009), 1007-1038 Request permission
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.References
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Additional Information
- Pavle V. M. Blagojević
- Affiliation: Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia
- Email: pavleb@mi.sanu.ac.yu
- Siniša T. Vrećica
- Affiliation: Mathematical Faculty, University of Belgrade, Belgrade, Serbia
- Email: vrecica@matf.bg.ac.yu
- Rade T. Živaljević
- Affiliation: Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia
- Email: rade@mi.sanu.ac.yu
- Received by editor(s): June 10, 2005
- Received by editor(s) in revised form: April 3, 2006, and May 7, 2007
- Published electronically: August 19, 2008
- Additional Notes: This research was supported by grants 144018 and 144026 of the Serbian Ministry of Science, Technology and Ecology.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 1007-1038
- MSC (2000): Primary 52A37, 55S35; Secondary 55M35
- DOI: https://doi.org/10.1090/S0002-9947-08-04679-5
- MathSciNet review: 2452832