Details
| Original language | English |
|---|---|
| Article number | e1010 |
| Journal | The Art of Discrete and Applied Mathematics |
| Volume | 1 |
| Issue number | 1 |
| Early online date | 10 Nov 2017 |
| Publication status | E-pub ahead of print - 10 Nov 2017 |
Abstract
A Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g - 1) automorphisms, where g is the genus of the surface. The Hurwitz surface of least genus is the Klein quartic of genus 3. A polyhedral realization without self-intersections of Klein's quartic of genus 3 was found by E. Schulte and J. M. Wills in 1985. For the next possible genus of a Hurwitz surface, i.e., for the genus 7 case with 72 vertices, we provide a polyhedral realization without self-intersections. We also show a topological representation for which we have a corresponding model.
Keywords
- Hurwitz surface, Polyhedral manifold, Regular map
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Computer Science(all)
- Computational Theory and Mathematics
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In: The Art of Discrete and Applied Mathematics, Vol. 1, No. 1, e1010, 10.11.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Hurwitz's regular map $(3,7)$ of genus 7: A polyhedral realization
AU - Bokowski, Jürgen
AU - Cuntz, Michael
PY - 2017/11/10
Y1 - 2017/11/10
N2 - A Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g - 1) automorphisms, where g is the genus of the surface. The Hurwitz surface of least genus is the Klein quartic of genus 3. A polyhedral realization without self-intersections of Klein's quartic of genus 3 was found by E. Schulte and J. M. Wills in 1985. For the next possible genus of a Hurwitz surface, i.e., for the genus 7 case with 72 vertices, we provide a polyhedral realization without self-intersections. We also show a topological representation for which we have a corresponding model.
AB - A Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g - 1) automorphisms, where g is the genus of the surface. The Hurwitz surface of least genus is the Klein quartic of genus 3. A polyhedral realization without self-intersections of Klein's quartic of genus 3 was found by E. Schulte and J. M. Wills in 1985. For the next possible genus of a Hurwitz surface, i.e., for the genus 7 case with 72 vertices, we provide a polyhedral realization without self-intersections. We also show a topological representation for which we have a corresponding model.
KW - Hurwitz surface
KW - Polyhedral manifold
KW - Regular map
UR - http://www.scopus.com/inward/record.url?scp=85096531862&partnerID=8YFLogxK
U2 - 10.26493/2590-9770.1186.258
DO - 10.26493/2590-9770.1186.258
M3 - Article
VL - 1
JO - The Art of Discrete and Applied Mathematics
JF - The Art of Discrete and Applied Mathematics
IS - 1
M1 - e1010
ER -