The automorphism group of compact Klein surfaces with one boundary component

1990 ◽  
pp. 138-152
Author(s):  
Emilio Bujalance ◽  
José Javier Etayo ◽  
José Manuel Gamboa ◽  
Grzegorz Gromadzki
Keyword(s):  
Automorphism Group ◽  
Boundary Component ◽  
Klein Surfaces

scholarly journals Complex doubles of bordered Klein surfaces with maximal symmetry

1991 ◽  
Vol 33 (1) ◽  
pp. 61-71 ◽  
Author(s):  
Coy L. May
Keyword(s):  
Automorphism Group ◽  
Special Interest ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Maximal Symmetry

A compact bordered Klein surface X of algebraic genus g ≥ 2 has maximal symmetry [6] if its automorphism group A(X) is of order 12(g — 1), the largest possible. The bordered surfaces with maximal symmetry are clearly of special interest and have been studied in several recent papers ([6] and [9] among others).

scholarly journals On the connectedness of the branch locus of moduli space of hyperelliptic Klein surfaces with one boundary

2017 ◽  
Vol 28 (05) ◽  
pp. 1750038 ◽  
Author(s):  
Antonio F. Costa ◽  
Milagros Izquierdo ◽  
Ana Maria Porto
Keyword(s):  
Moduli Space ◽  
Boundary Component ◽  
Branch Locus ◽  
Klein Surfaces ◽  
Genus Formula

In this work, we prove that the hyperelliptic branch locus of orientable Klein surfaces of genus [Formula: see text] with one boundary component is connected and in the case of non-orientable Klein surfaces it has [Formula: see text] components, if [Formula: see text] is odd, and [Formula: see text] components for even [Formula: see text]. We notice that, for non-orientable Klein surfaces with two boundary components, the hyperelliptic branch loci are connected for all genera.

scholarly journals On the automorphism group of hyperelliptic Klein surfaces.

1988 ◽  
Vol 35 (3) ◽  
pp. 361-368 ◽  
Author(s):  
E. Bujalance ◽  
J. A. Bujalance ◽  
E. Martínez
Keyword(s):  
Automorphism Group ◽  
Klein Surfaces

scholarly journals Topological types of Klein surfaces with a maximum order automorphism

1988 ◽  
Vol 30 (1) ◽  
pp. 87-96
Author(s):  
J. A. Bujalance
Keyword(s):  
Boundary Component ◽  
Topological Type ◽  
Klein Surface ◽  
Maximum Order ◽  
Klein Surfaces ◽  
Order Automorphism

If X is a Klein surface (KS) with boundary, of algebraic genus p, and Φ is an automorphism of order N, May [8] proved that N ≤ 2p + 2 when X is orientable and p is even, and N ≤ 2p otherwise.He proved also that the unique topological type of an orientable KS having an orientation-preserving automorphism of maximum order is a surface with one boundary component when p is even, with two boundary components when p is odd.

THE SYMMETRIC CROSSCAP NUMBER OF THE GROUPS OF SMALL-ORDER

2012 ◽  
Vol 12 (02) ◽  
pp. 1250164 ◽  
Author(s):  
J. J. ETAYO ◽  
E. MARTÍNEZ
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
The Other ◽  
Klein Surfaces ◽  
Exceptional Groups ◽  
Minimal Genus ◽  
Other Hand ◽  
Unique Integer ◽  
Symmetric Crosscap Number

Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric crosscap number and denoted by [Formula: see text]. It is known that 3 cannot be the symmetric crosscap number of a group. Conversely, it is also known that all integers that do not belong to nine classes modulo 144 are the symmetric crosscap number of some group. Here we obtain infinitely many groups whose symmetric crosscap number belong to each one of six of these classes. This result supports the conjecture that 3 is the unique integer which is not the symmetric crosscap number of a group. On the other hand, there are infinitely many groups with symmetric crosscap number 1 or 2. For g > 2 the number of groups G with [Formula: see text] is finite. The value of [Formula: see text] is known when G belongs to certain families of groups. In particular, if o(G) < 32, [Formula: see text] is known for all except thirteen groups. In this work we obtain it for these groups by means of a one-by-one analysis. Finally we obtain the least genus greater than two for those exceptional groups whose symmetric crosscap number is 1 or 2.

The automorphism group of hyperelliptic compact Klein surfaces with boundary

1990 ◽  
pp. 153-164
Author(s):  
Emilio Bujalance ◽  
José Javier Etayo ◽  
José Manuel Gamboa ◽  
Grzegorz Gromadzki
Keyword(s):  
Automorphism Group ◽  
Klein Surfaces

The symmetric cross-cap number of the groups Cm × Dn

2008 ◽  
Vol 138 (6) ◽  
pp. 1197-1213 ◽  
Author(s):  
J. J. Etayo Gordejuela ◽  
E. Martínez
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Finite Groups ◽  
Systematic Study ◽  
Klein Surfaces ◽  
Minimal Genus ◽  
Arithmetic Sequences ◽  
Sigma G

Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric cross-cap number and denoted by $\tilde{\sigma}(G)$. This number is related to other parameters defined on surfaces as the symmetric genus and the strong symmetric genus.The systematic study of the symmetric cross-cap number was begun by C. L. May, who also calculated it for certain finite groups. Here we obtain the symmetric cross-cap number for the groups Cm × Dn. As an application of this result, we obtain arithmetic sequences of integers which are the symmetric cross-cap number of some group. Finally, we recall the several different genera of the groups Cm × Dn.

scholarly journals q-hyperelliptic compact nonorientable Klein surfaces without boundary

2002 ◽  
Vol 31 (4) ◽  
pp. 215-227
Author(s):  
J. A. Bujalance ◽  
B. Estrada
Keyword(s):  
Automorphism Group ◽  
Riemann Surfaces ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Crystallographic Groups ◽  
Nonorientable Surface

LetXbe a nonorientable Klein surface (KS in short), that is a compact nonorientable surface with a dianalytic structure defined on it. A Klein surfaceXis said to beq-hyperellipticif and only if there exists an involutionΦonX(a dianalytic homeomorphism of order two) such that the quotientX/〈Φ〉has algebraic genusq.q-hyperelliptic nonorientable KSs without boundary (nonorientable Riemann surfaces) were characterized by means of non-Euclidean crystallographic groups. In this paper, using that characterization, we determine bounds for the order of the automorphism group of a nonorientableq-hyperelliptic Klein surfaceXsuch thatX/〈Φ〉has no boundary and prove that the bounds are attained. Besides, we obtain the dimension of the Teichmüller space associated to this type of surfaces.

Sign in / Sign up

Export Citation Format

Share Document