The Experts below are selected from a list of 135 Experts worldwide ranked by ideXlab platform
Blazej Szepietowski - One of the best experts on this subject based on the ideXlab platform.
-
generating the mapping class group of a Nonorientable Surface by three torsions
arXiv: Geometric Topology, 2020Co-Authors: Marta Leśniak, Blazej SzepietowskiAbstract:We prove that the mapping class group $\mathcal{M}(N_g)$ of a closed Nonorientable Surface of genus $g$ different than 4 is generated by three torsion elements. Moreover, for every even integer $k\ge 12$ and $g$ of the form $g=pk+2q(k-1)$ or $g=pk+2q(k-1)+1$, where $p,q$ are non-negative integers and $p$ is odd, $\mathcal{M}(N_g)$ is generated by three conjugate elements of order $k$. Analogous results are proved for the subgroup of $\mathcal{M}(N_g)$ generated by Dehn twists.
-
generating the mapping class group of a Nonorientable Surface by crosscap transpositions
Topology and its Applications, 2017Co-Authors: Marta Leśniak, Blazej SzepietowskiAbstract:Abstract 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 crosscaps. We prove that the mapping class group of a compact Nonorientable Surface of genus g ≥ 7 is generated by conjugates of one crosscap transposition. In the case when the Surface is either closed or has one boundary component, we give an explicit set of g + 2 crosscap transpositions generating the mapping class group.
-
Automorphisms of the mapping class group of a Nonorientable Surface
Geometriae Dedicata, 2017Co-Authors: Ferihe Atalan, Blazej SzepietowskiAbstract:Let S be a Nonorientable Surface of genus $$g\ge 5$$ g ≥ 5 with $$n\ge 0$$ n ≥ 0 punctures, and $$\mathrm {Mod}(S)$$ Mod ( S ) its mapping class group. We define the complexity of S to be the maximum rank of a free abelian subgroup of $$\mathrm {Mod}(S)$$ Mod ( S ) . Suppose that $$S_1$$ S 1 and $$S_2$$ S 2 are two such Surfaces of the same complexity. We prove that every isomorphism $$\mathrm {Mod}(S_1)\rightarrow \mathrm {Mod}(S_2)$$ Mod ( S 1 ) → Mod ( S 2 ) is induced by a diffeomorphism $$S_1\rightarrow S_2$$ S 1 → S 2 . This is an analogue of Ivanov’s theorem on automorphisms of the mapping class groups of an orientable Surface, and also an extension and improvement of the first author’s previous result.
-
generating the mapping class group of a Nonorientable Surface by crosscap transpositions
arXiv: Geometric Topology, 2017Co-Authors: Marta Leśniak, Blazej SzepietowskiAbstract: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 crosscaps. We prove that the mapping class group of a compact Nonorientable Surface of genus $g\ge 7$ is generated by conjugates of one crosscap transposition. In the case when the Surface is either closed or has one boundary component, we give an explicit set of $g+2$ crosscap transpositions generating the mapping class group.
-
on finite index subgroups of the mapping class group of a Nonorientable Surface
Glasnik Matematicki, 2014Co-Authors: Blazej SzepietowskiAbstract:Let $M(N_{h,n})$ denote the mapping class group of a compact Nonorientable Surface of genus $h\ge 7$ and $n\le 1$ boundary components, and let $T(N_{h,n})$ be the subgroup of $M(N_{h,n})$ generated by all Dehn twists. It is known that $T(N_{h,n})$ is the unique subgroup of $M(N_{h,n})$ of index $2$. We prove that $T(N_{h,n})$ (and also $M(N_{h,n})$) contains a unique subgroup of index $2^{g-1}(2^g-1)$ up to conjugation, and a unique subgroup of index $2^{g-1}(2^g+1)$ up to conjugation, where $g=\lfloor(h-1)/2\rfloor$. The other proper subgroups of $T(N_{h,n})$ and $M(N_{h,n})$ have index greater than $2^{g-1}(2^g+1)$. In particular, the minimum index of a proper subgroup of $T(N_{h,n})$ is $2^{g-1}(2^g-1)$.
Michal Stukow - One of the best experts on this subject based on the ideXlab platform.
-
the hyperelliptic mapping class group of a Nonorientable Surface of genus g 4 has a faithful representation into gl g2 1 r
Comptes Rendus Mathematique, 2016Co-Authors: Michal StukowAbstract:Abstract We prove that the hyperelliptic mapping class group of a Nonorientable Surface of genus g ≥ 4 has a faithful linear representation of dimension g 2 − 1 over R .
-
the hyperelliptic mapping class group of a Nonorientable Surface of genus g geq 4 has a faithful representation into gl g 2 1 mathbb r
arXiv: Geometric Topology, 2016Co-Authors: Michal StukowAbstract:We prove that the hyperelliptic mapping class group of a Nonorientable Surface of genus $g\geq 4$ has a faithful linear representation of dimension $g^2-1$ over $\mathbb{R}$.
-
a finite presentation for the twist subgroup of the mapping class group of a Nonorientable Surface
Bulletin of The Korean Mathematical Society, 2016Co-Authors: Michal StukowAbstract:Let Ng;s denote the Nonorientable Surface of genus g with s bound- ary components. Recently Paris and Szepietowski (12) obtained an explicit nite presentation for the mapping class group M(Ng;s) of the Surface Ng;s, where s 2 f0; 1g and g + s > 3. Following this work we obtain a nite presen- tation for the subgroup T (Ng;s) of M(Ng;s) generated by Dehn twists.
-
the first homology group of the mapping class group of a Nonorientable Surface with twisted coefficients
Topology and its Applications, 2014Co-Authors: Michal StukowAbstract:Abstract We determine the first homology group of the mapping class group M ( N ) of a Nonorientable Surface N with coefficients in H 1 ( N ; Z ) .
-
a finite presentation for the mapping class group of a Nonorientable Surface with dehn twists and one crosscap slide as generators
Journal of Pure and Applied Algebra, 2014Co-Authors: Michal StukowAbstract:Abstract Let N g , s denote the Nonorientable Surface of genus g with s boundary components. Recently Paris and Szepietowski [14] obtained an explicit finite presentation for the mapping class group M ( N g , s ) of the Surface N g , s , where s ∈ { 0 , 1 } and g + s > 3 . Following this work we obtain a finite presentation for the mapping class group M ( N g , s ) with generators being Dehn twists and one crosscap slide.
Strenner Balázs - One of the best experts on this subject based on the ideXlab platform.
-
Minimal pseudo-Anosov stretch factors on nonoriented Surfaces
2020Co-Authors: Liechti Livio, Strenner BalázsAbstract:We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed Nonorientable Surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliations on the closed orientable Surfaces of genus 1, 3, 5, 7, 9 and 11. As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a Nonorientable Surface or an orientation-reversing pseudo-Anosov map on an orientable Surface does not have Galois conjugates on the unit circle. This shows that the techniques that were used to disprove Penner’s conjecture on orientable Surfaces are ineffective in the Nonorientable cases
-
Minimal pseudo-Anosov stretch factors on nonoriented Surfaces
'Mathematical Sciences Publishers', 2020Co-Authors: Liechti Livio, Strenner BalázsAbstract:We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed Nonorientable Surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliations on the closed orientable Surfaces of genus 1, 3, 5, 7, 9 and 11. As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a Nonorientable Surface or an orientation-reversing pseudo-Anosov map on an orientable Surface does not have Galois conjugates on the unit circle. This shows that the techniques that were used to disprove Penner's conjecture on orientable Surfaces are ineffective in the Nonorientable cases.Comment: 26 pages, 6 figure
Thomas John Baird - One of the best experts on this subject based on the ideXlab platform.
-
antiperfection of yang mills morse theory over a Nonorientable Surface
International Journal of Mathematics, 2015Co-Authors: Thomas John BairdAbstract:We use Morse theory of the Yang–Mills functional to compute the Betti numbers of the moduli stack of flat U(3)-bundles over a compact Nonorientable Surface. Our result establishes the antiperfection conjecture of Ho–Liu, and establishes the equivariant formality conjecture of the author for U(3)-bundles.
-
antiperfection of yang mills morse theory over a Nonorientable Surface
arXiv: Symplectic Geometry, 2009Co-Authors: Thomas John BairdAbstract:We use Morse theory of the Yang-Mills functional to compute the Betti numbers of the moduli stack of flat U(3)-bundles over a compact Nonorientable Surface. Our result establishes the antiperfection conjecture of Ho-Liu, and provides evidence for the equivariant formality conjecture of the author.
-
antiperfection of yang mills morse theory over a Nonorientable Surface in rank three
2009Co-Authors: Thomas John BairdAbstract:We use Morse theory of the Yang-Mills functional to compute the Betti numbers of the moduli stack of flat U(3)-bundles over a compact Nonorientable Surface. Our result establishes the antiperfection conjecture of Ho-Liu, and provides evidence for the equivariant formality conjecture of the author.
Liechti Livio - One of the best experts on this subject based on the ideXlab platform.
-
Minimal pseudo-Anosov stretch factors on nonoriented Surfaces
2020Co-Authors: Liechti Livio, Strenner BalázsAbstract:We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed Nonorientable Surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliations on the closed orientable Surfaces of genus 1, 3, 5, 7, 9 and 11. As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a Nonorientable Surface or an orientation-reversing pseudo-Anosov map on an orientable Surface does not have Galois conjugates on the unit circle. This shows that the techniques that were used to disprove Penner’s conjecture on orientable Surfaces are ineffective in the Nonorientable cases
-
Minimal pseudo-Anosov stretch factors on nonoriented Surfaces
'Mathematical Sciences Publishers', 2020Co-Authors: Liechti Livio, Strenner BalázsAbstract:We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed Nonorientable Surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliations on the closed orientable Surfaces of genus 1, 3, 5, 7, 9 and 11. As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a Nonorientable Surface or an orientation-reversing pseudo-Anosov map on an orientable Surface does not have Galois conjugates on the unit circle. This shows that the techniques that were used to disprove Penner's conjecture on orientable Surfaces are ineffective in the Nonorientable cases.Comment: 26 pages, 6 figure
