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 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 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

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 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.

scholarly journals ALGEBRAIC CURVES, RIEMANN SURFACES AND KLEIN SURFACES WITH NO NON-TRIVIAL AUTOMORPHISMS OR SYMMETRIES

2002 ◽  
Vol 45 (1) ◽  
pp. 141-148 ◽  
Author(s):  
Peter Turbek
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Characteristic Zero ◽  
Riemann Surfaces ◽  
Algebraic Curves ◽  
Klein Surfaces ◽  
New Family ◽  
Family Of Curves ◽  
Primary 14H37 ◽  
The Family

AbstractThe explicit defining equations of a new family of curves whose members have a trivial automorphism group are given. Each member is defined for characteristic zero and all but a finite number of characteristics greater than zero. This family, in conjunction with a previously appearing family of the author’s, provides explicit examples of algebraic curves which possess only the trivial automorphism for each genus greater than three. The family is then used to construct Riemann surfaces without anticonformal automorphisms and Klein surfaces with no non-trivial automorphisms.AMS 2000 Mathematics subject classification: Primary 14H37; 30F50; 30F99

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

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