Lifting the hyperelliptic involution of a Klein surface

2018 ◽  
Vol 31 (3) ◽  
pp. 611-626
Author(s):  
Emilio Bujalance ◽  
Francisco-Javier Cirre ◽  
Peter Turbek
Keyword(s):  
Klein Surface ◽  
Hyperelliptic Involution

scholarly journals DOUBLES OF KLEIN SURFACES

2012 ◽  
Vol 54 (3) ◽  
pp. 507-515
Author(s):  
ANTONIO F. COSTA ◽  
WENDY HALL ◽  
DAVID SINGERMAN
Keyword(s):  
Klein Bottle ◽  
Orientable Surface ◽  
Historical Note ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Algebraic Functions ◽  
Genus 2

Historical note. A non-orientable surface of genus 2 (meaning 2 cross-caps) is popularly known as the Klein bottle. However, the term Klein surface comes from Felix Klein's book “On Riemann's Theory of Algebraic Functions and their Integrals” (1882) where he introduced such surfaces in the final chapter.

scholarly journals A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group

2009 ◽  
Vol 146 (1) ◽  
pp. 109-118 ◽  
Author(s):  
YUSUKE KUNO
Keyword(s):  
Mapping Class Group ◽  
Homology Group ◽  
Class Group ◽  
Base Point ◽  
Mapping Class ◽  
Combinatorial Formula ◽  
Hyperelliptic Involution ◽  
Fixed Base ◽  
Genus 2 ◽  
Closed Oriented Surface

AbstractWe present a formula expressing Earle's twisted 1-cocycle on the mapping class group of a closed oriented surface of genus ≥ 2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita's twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class group, which is topologically a hyperelliptic involution.

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).

RESIDUES ON A KLEIN SURFACE

2007 ◽  
Author(s):  
ARTURO FERNÁNDEZ ÁRIAS ◽  
JAVIER PÉREZ ALVAREZ
Keyword(s):  
Klein Surface

Groups of real genus p + 1, where p is prime

2014 ◽  
Vol 14 (03) ◽  
pp. 1550040
Author(s):  
Coy L. May
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Klein Surface ◽  
The Real ◽  
A Finite Group ◽  
Large Groups

Let G be a finite group. The real genusρ(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. We classify the large groups of real genus p + 1, that is, the groups such that |G| ≥ 3(g - 1), where the genus action of G is on a bordered surface of genus g = p + 1. The group G must belong to one of four infinite families. In addition, we determine the order of the largest automorphism group of a surface of genus g for all g such that g = p + 1, where p is a prime.

scholarly journals Moduli spaces of vector bundles over a Klein surface

2010 ◽  
Vol 151 (1) ◽  
pp. 187-206 ◽  
Author(s):  
Florent Schaffhauser
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Klein Surface

THE REAL GENUS OF 2-GROUPS

2007 ◽  
Vol 06 (01) ◽  
pp. 103-118 ◽  
Author(s):  
COY L. MAY
Keyword(s):  
Finite Group ◽  
Klein Surface ◽  
Positive Real ◽  
Klein Surfaces ◽  
The Real ◽  
A Finite Group

Let G be a finite group. The real genus ρ(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. Here we consider 2-groups acting on bordered Klein surfaces. The main focus is determining the real genus of each of the 51 groups of order 32. We also obtain some general results about the partial presentations that 2-groups acting on bordered surfaces must have. In addition, we obtain genus formulas for some families of 2-groups and show that if G is a 2-group with positive real genus, then ρ(G) ≡ 1 mod 4.

scholarly journals Supersolvable M*-groups

1988 ◽  
Vol 30 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Coy L. May
Keyword(s):  
Automorphism Group ◽  
Klein Surface ◽  
Maximal Symmetry

A compact bordered Klein surface of genus g ≥ 2 has maximal symmetry [4] if its automorphism group is of order 12(g − 1), the largest possible. An M*-group [8] acts on a bordered surface with maximal symmetry. The first important result about these groups was that they must have a certain partial presentation [8, p. 5]. However, research has tended to focus more on the surfaces with maximal symmetry than on the M*-groups, and results about these groups typically deal with existence.

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