Gluing of Surfaces with Polygonal Boundaries
| dc.creator | Akhmedov, E. T. | |
| dc.creator | Shakirov, Sh. | |
| dc.date | 2007-12-17 | |
| dc.date | 2008-08-24 | |
| dc.date.accessioned | 2026-07-07T09:57:47Z | |
| dc.date.available | 2026-07-07T09:57:47Z | |
| dc.description | By pairwise gluing of edges of a polygon, one produces two-dimensional surfaces with handles and boundaries. In this paper, we count the number ${\cal N}_{g,L}(n_1, n_2, ..., n_L)$ of different ways to produce a surface of given genus $g$ with $L$ polygonal boundaries with given numbers of edges $n_1, n_2, >..., n_L$. Using combinatorial relations between graphs on real two-dimensional surfaces, we derive recursive relations between ${\cal N}_{g,L}$. We show that Harer-Zagier numbers appear as a particular case of ${\cal N}_{g,L}$ and derive a new explicit expression for them. | |
| dc.description | 7 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0712.2448 | |
| dc.identifier | http://arxiv.org/abs/0712.2448 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167473 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.title | Gluing of Surfaces with Polygonal Boundaries | |
| dc.type | text |