Equipartitions of measures in $\mathbb{R}^4$
| dc.creator | Zivaljevic, Rade T. | |
| dc.date | 2004-12-23 | |
| dc.date.accessioned | 2026-07-07T05:15:38Z | |
| dc.date.available | 2026-07-07T05:15:38Z | |
| dc.description | We prove that each measure $μ$ in $R^4$ admits an equipartition by 4 hyperplanes, provided that it is symmetric with respect to a 2-dimensional, affine subspace $L$ of $R^4$. Moreover we show, by computing the complete obstruction in the relevant group of normal bordisms, that without the symmetry condition, a naturally associated topological problem has a negative solution. The computation is based on the Koschorke's exact singularity sequence and the remarkable properties of the essentially unique, balanced binary Gray code in dimension 4. | |
| dc.identifier | https://arxiv.org/abs/math/0412483 | |
| dc.identifier | http://arxiv.org/abs/math/0412483 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73694 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 52A38; 52A39; 52C35; 55S40; 57R25; 57R85; 57S25; 68P05; 68P30; 68R05 | |
| dc.title | Equipartitions of measures in $\mathbb{R}^4$ | |
| dc.type | text |