Symmetric products of surfaces and the cycle index
| dc.creator | Blagojevic, Pavle | |
| dc.creator | Grujic, Vladimir | |
| dc.creator | Zivaljevic, Rade | |
| dc.date | 2003-06-27 | |
| dc.date.accessioned | 2026-07-07T04:59:14Z | |
| dc.date.available | 2026-07-07T04:59:14Z | |
| dc.description | We express the signature ${\rm Sign}(SP^m_G(M))$ of the symmetric product $SP^n(M)$ of an (open) surface $M$ in terms of the cycle index $Z(G;\bar x)$ of $G$, a polynomial which originally appeared in P{\' o}lya enumeration theory of graphs, trees, chemical structures etc. The computations are used to show that there exist punctured Riemann surfaces $M_{g,k}, M_{g',k'}$ such that the manifolds $SP^{m}(M_{g,k})$ and $SP^{m}(M_{g',k'})$ are often not homeomorphic, although they always have the same homotopy type provided $2g+k = 2g'+k'$ and $k,k'\geq 1$. | |
| dc.identifier | https://arxiv.org/abs/math/0306397 | |
| dc.identifier | http://arxiv.org/abs/math/0306397 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67905 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55S15; 14H40, 55R80, 57R19 | |
| dc.title | Symmetric products of surfaces and the cycle index | |
| dc.type | text |