19 citations · 58 across the 16 of their papers we have counts for
16 papers
The pants graph as a combinatorial model for the Teichmüller space of a non-orientable surface
Michał Stukow, Błażej Szepietowski, Jakub Szmelter-Tomczuk
We study the relation between the pants graph of a non-orientable surface and that of its orientable double cover. Given a non-orientable surface with orientable double cover $…
Automorphisms of the pants graph of a nonorientable surface
Michał Stukow, Błażej Szepietowski
We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class gro…
Geometric representations of the braid group on a nonorientable surface
Michał Stukow, Błażej Szepietowski
We classify homomorphisms from the braid group on strands to the pure mapping class group of a nonoriantable surface of genus . For and $g\le 2\lfloor{n/2}\rfloor+…
Generating the mapping class group of a nonorientable surface by three torsions
Marta Leśniak, Błażej Szepietowski
We prove that the mapping class group of a closed nonorientable surface of genus different than 4 is generated by three torsion elements. Moreover, for every…
A note on the curve complex of the 3-holed projective plane
Błażej Szepietowski
Let be a projective plane with holes. We prove that there is an exhaustion of the curve complex by a sequence of finite rigid sets. As a corollary, we obta…
Generating the mapping class group of a nonorientable surface by crosscap transpositions
Marta Leśniak, Błażej Szepietowski
A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two c…
On topological classification of finite cyclic actions on bordered surfaces
Grzegorz Gromadzki, Susumu Hirose, Błażej Szepietowski
In [Tohoku Math. J. 62 (2010), 45--53] the second author showed that, except for a few cases, the order of a cyclic group of self-homeomorphisms of a closed orientable topologi…
Automorphisms of the mapping class group of a nonorientable surface
Ferihe Atalan, Błażej Szepietowski
Let be a nonorientable surface of genus with punctures, and $\Mcg(S)$ its mapping class group. We define the complexity of to be the maximum rank of a fre…
On finite index subgroups of the mapping class group of a nonorientable surface
Blazej Szepietowski
Let denote the mapping class group of a compact nonorientable surface of genus and boundary components, and let be the subgroup of $M(N_…
A presentation for the mapping class group of a nonorientable surface
Luis Paris, Blazej Szepietowski
Let denote the nonorientable surface of genus with boundary components and its mapping class group. We obtain an explicit finite presentation of $M(N…
Low dimensional linear representations of the mapping class group of a nonorientable surface
Blazej Szepietowski
Suppose that is a homomorphism from the mapping class group of a nonorientable surface of genus with boundary components, to $\mathrm{GL}(m,\math…
A finite generating set for the level 2 mapping class group of a nonorientable surface
Blazej Szepietowski
We obtain a finite set of generators for the level 2 mapping class group of a closed nonorientable surface of genus . This set consists of isotopy classes of Lickorish's Y-…
On the commutator length of a Dehn twist
Blazej Szepietowski
We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additio…
Crosscap slides and the level 2 mapping class group of a nonorientable surface
Blazej Szepietowski
Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of th…
A presentation for the mapping class group of the closed non-orientable surface of genus 4
Błażej Szepietowski
Finite presentations for the mapping class group M(F) are known for arbitrary orientable compact surface F. If F is non-orientable, then such presentations are known only when F ha…
A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves
Błażej Szepietowski
We study the action of the mapping class group M(F) on the complex of curves of a non-orientable surface F. We obtain, by using a result of K. S. Brown, a presentation for M(F) def…