Asymmetric combinatorially-regular maps
Marston Conder
University of Auckland Department of Mathematics Private Bag 92019 Auckland New Zealand Private Bag 92019 Auckland New Zealand
DOI: 10.1007/BF00193182
Abstract
It is shown that for every g\geq 3, there exists a combinatorially regular map M of type (3, 7) on a closed orientable surface of genus g, such that M has trivial symmetry group. Such maps are constructed from Schreier coset graphs corresponding to permutation representations of the (2, 3, 7) triangle group.
1991 Mathematics Subject Classification: 57M15.
Pages: 323–328
Full Text: PDF
References
M.D.E.Conder, “Generators for alternating and symmetric groups,” J. London Math. Soc. $( 2) 22$ (1980), 75-86. H.S.M.Coxeter and W.O.J.Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, Berlin,
1980. P.Schmutz, “Systoles on Riemann surfaces,” Manuscripta Mathematica 85 (1994), 429-447. S.E.Wilson, “Operators over regular maps,” Pacific J. Math. 81 (1979), 559-568. S.E.Wilson, “Cantankerous maps and rotary embeddings of $K _{n}$,” J. Combin. Theory Series B 47 (1989), 262-273.
1980. P.Schmutz, “Systoles on Riemann surfaces,” Manuscripta Mathematica 85 (1994), 429-447. S.E.Wilson, “Operators over regular maps,” Pacific J. Math. 81 (1979), 559-568. S.E.Wilson, “Cantankerous maps and rotary embeddings of $K _{n}$,” J. Combin. Theory Series B 47 (1989), 262-273.