Extensions of finite cyclic group actions on non-orientable surfaces

Bujalance, E.; Cirre, Francisco-Javier; Conder, Marston

doi:10.1090/s0002-9947-2013-05776-5

Cited by 10 publications

(35 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, which means that either p = 2 or ( p, q) ∈ {(3, 3), (3,4), (3, 5)}. We fix NEC groups 1 and 2 with signatures (0; +; [2, p, q]; {( )}) and (1; −; [2, p, q]; {−}), denoted respectively by σ 1 and σ 2 .…”

Section: Actions With 3-punctured Disc or Projective Plane As The Quomentioning

confidence: 99%

“…The case g = 3 is well understood, as the mapping class group of S 3 is isomorphic to GL 2 (Z) (see [8]), and the classification of conjugacy classes of torsion elements in the latter group is known. Another interesting problem concerning cyclic periodic actions on non-orientable surfaces was considered in recent paper [3], where the authors investigated such actions which can not be extended to any bigger group.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On topological type of periodic self-homeomorphisms of closed non-orientable surfaces

Gromadzki

Szepietowski

2015

RACSAM

View full text Add to dashboard Cite

Let S g denote a closed non-orientable surface of genus g ≥ 3. At the beginning of 1980s E. Bujalance showed that the maximum order of a periodic self-homeomorphism of S g is equal to 2g or 2(g − 1) for g odd or even respectively, and this upper bound is attained for all g ≥ 3. In this paper we enumerate, up to topological conjugation, actions on S g of a cyclic group Z N of order N > g − 2 with prescribed type of the quotient orbifold S g /Z N . We also compute, for a fixed g and N ranging between max{g, 3(g − 2)/2} and 2g, the total numbers of different topological types of action of Z N on S g .

show abstract

Section: Actions With 3-punctured Disc or Projective Plane As The Quomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On topological type of periodic self-homeomorphisms of closed non-orientable surfaces

Gromadzki

Szepietowski

2015

RACSAM

View full text Add to dashboard Cite

show abstract

“…Recall from Theorems 2.1 and 2.2 that, in the case of Riemann surfaces, the extendability of a cyclic action depends on the signature and on the surface-kernel epimorphism. In the case of cyclic group actions on non-orientable unbordered surfaces, the situation is surprisingly quite different, as the next theorem, proved in [9], shows.…”

Section: Extendability Of Group Actions On Klein Surfacesmentioning

confidence: 98%

Groups of automorphisms of Riemann and Klein surfaces, our joint work with Marston Conder

Bujalance

Cirre

2022

Art Discrete Appl. Math.

View full text Add to dashboard Cite

show abstract

“…where each cone point of order 2 is produced by a fixed point of one of the involutions yz 4t , with 0 ≤ t ≤ 2n − 1; each cone point of order 4 is produced by a fixed point of yz 4l+2 , with 0 ≤ l ≤ 2n − 1; and each point of order δ j is produced by a fixed point of some element in z 2 (i.e., δ j ≥ 2, δ j |4n). By the Riemann-Hurwitz formula we have (12) 2(g − 1) = 16n(γ − 1)…”

Section: 22mentioning

confidence: 99%