Authors: | Blagojević, Pavle Ziegler, Günter |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes | Journal: | Topology and its Applications | Volume: | 158 | Issue: | 12 | First page: | 1326 | Last page: | 1351 | Issue Date: | 1-Aug-2011 | Rank: | M23 | ISSN: | 0166-8641 | DOI: | 10.1016/j.topol.2011.05.008 | Abstract: | We compute the complete Fadell-Husseini index of the dihedral group D8=(Z{double-struck}2)2⋊Z{double-struck}2 acting on Sd×Sd for F{double-struck}2 and for Z{double-struck} coefficients, that is, the kernels of the maps in equivariant cohomology. HD8*(pt,F{double-struck}2)→HD8*(Sd×Sd,F{double-struck}2) and. HD8*(pt,Z{double-struck})→HD8*(Sd×Sd,Z{double-struck}). This establishes the complete cohomological lower bounds, with F{double-struck}2 and with Z{double-struck} coefficients, for the two-hyperplane case of Grünbaum's 1960 mass partition problem: For which d and j can any j arbitrary measures be cut into four equal parts each by two suitably chosen hyperplanes in R{double-struck}d? In both cases, we find that the ideal bounds are not stronger than previously established bounds based on one of the maximal abelian subgroups of D8. |
Keywords: | Bockstein spectral sequence | Dihedral group | Equivariant cohomology | Fadell-Husseini index | Mass partitions | Serre spectral sequence | Publisher: | Elsevier | Project: | European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC, Grant agreement No. 247029-SDModels Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security |
Show full item record
SCOPUSTM
Citations
20
checked on Nov 18, 2024
Page view(s)
17
checked on Nov 19, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.