Topology of partition of measures by fans and the second obstruction
| dc.creator | Blagojevic, Pavle V. M. | |
| dc.date | 2004-02-25 | |
| dc.date | 2004-07-27 | |
| dc.date.accessioned | 2026-07-07T05:05:42Z | |
| dc.date.available | 2026-07-07T05:05:42Z | |
| dc.description | \noindent The simultaneous partition problems are classical problems of the combinatorial geometry which have the natural flavor of the equivariant topology. The $k$-fan partition problems have attracted a lot of attention \cite{Aki2000}, \cite{BaMa2001}, \cite{BaMa2002} and forced some hard concrete combinatorial calculations in the equivariant cohomology \cite% {Bl-Vr-Ziv}. These problems can be reduced, by a beautiful scheme of \cite% {BaMa2001}, to a \textquotedblright typical\textquotedblright question of the existence of a $\mathbb{D}_{2n}$ equivariant map $f:V_{2}(\mathbb{R}% ^{3})\to W_{n}-\cup \mathcal{A}(α)$, where $V_{2}(\mathbb{R}% ^{3})$ is the space of all orthonormal 2-frames in $\mathbb{R}^{3}$ and $% W_{n}-\cup \mathcal{A}(α)$ is the complement of the appropriate arrangement. We introduce the \textit{target extension scheme} which allow us to use the equivariant obstruction theory as a tool for proving that: for every two proper measures on the sphere $S^{2}$, and any $α=(a,a+b,b)\in \mathbb{R}_{>0}^{3}$, there exists an $α$-partition of theses measures by a 3-fan. \noindent The significance of these results, among other, is that, beside negative results \cite{Bl-Vr-Ziv}, the equivariant obstruction theory can pull off some positive results, which were not attained by other means. | |
| dc.description | The exposition is radicaly improved. The proof is more general. The obstruction cocycle got the clear geometric interpretation | |
| dc.identifier | https://arxiv.org/abs/math/0402400 | |
| dc.identifier | http://arxiv.org/abs/math/0402400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70267 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 52C15; 55S91 | |
| dc.title | Topology of partition of measures by fans and the second obstruction | |
| dc.type | text |