Polyhedral surfaces of high genus
| dc.creator | Ziegler, Günter M. | |
| dc.date | 2004-12-05 | |
| dc.date.accessioned | 2026-07-07T05:14:57Z | |
| dc.date.available | 2026-07-07T05:14:57Z | |
| dc.description | The construction of the COMBINATORIAL data for a surface with n vertices of maximal genus is a classical problem: The maximal genus g=[(n-3)(n-4)/12] was achieved in the famous ``Map Color Theorem'' by Ringel et al. (1968). We present the nicest one of Ringel's constructions, for the case when n is congruent to 7 mod 12, but also an alternative construction, essentially due to Heffter (1898), which easily and explicitly yields surfaces of genus g ~ 1/16 n^2. For GEOMETRIC (polyhedral) surfaces with n vertices the maximal genus is not known. The current record is g ~ n log n, due to McMullen, Schulz & Wills (1983). We present these surfaces with a new construction: We find them in Schlegel diagrams of ``neighborly cubical 4-polytopes,'' as constructed by Joswig & Ziegler (2000). | |
| dc.description | 21 pages; Lecture Notes for Oberwolfach Seminar "Discrete Differential Geometry", June 2004 | |
| dc.identifier | https://arxiv.org/abs/math/0412093 | |
| dc.identifier | http://arxiv.org/abs/math/0412093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73483 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 52B70 | |
| dc.title | Polyhedral surfaces of high genus | |
| dc.type | text |