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Let $N_{g,s}$ denote the nonorientable surface of genus $g$ with $s$ boundary components. Recently Paris and Szepietowski \cite{SzepParis} obtained an explicit finite presentation for the mapping class group $\cM(N_{g,s})$ of the surface $N_{g,s}$, where $s\in\{0,1\}$ and $g+s>3$. Following this work, we obtain a finite presentation for the subgroup $\cT(N_{g,s})$ of $\cM(N_{g,s})$ generated by Dehn twists.
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참고문헌 (16)
참고문헌 신청
J. S. Birman / 1969 / Automorphisms of the fundamental group of a closed, orientable 2-manifold / Proc. Amer. Math. Soc 21(2):351~354
D. R. J. Chillingworth / 1969 / A finite set of generators for the homeotopy group of a non{orientable surface / Math. Proc. Cambridge Philos. Soc 65:409~430
S. Gervais / 2001 / A finite presentation of the mapping class group of a punctured surface / Topology 40(4):703~725
S. P. Humphries / 1979 / Generators for the mapping class group / Topology of low-dimensional manifolds (Proc. Second Sussex Conf) :44~47
D. L. Johnson / 1979 / Homeomorphisms of a surface which act trivially on homology / Proc. Amer. Math. Soc 75(1):119~125
D. R. J. Chillingworth / 1969 / A finite set of generators for the homeotopy group of a non{orientable surface / Math. Proc. Cambridge Philos. Soc 65:409~430
S. Gervais / 2001 / A finite presentation of the mapping class group of a punctured surface / Topology 40(4):703~725
S. P. Humphries / 1979 / Generators for the mapping class group / Topology of low-dimensional manifolds (Proc. Second Sussex Conf) :44~47
D. L. Johnson / 1979 / Homeomorphisms of a surface which act trivially on homology / Proc. Amer. Math. Soc 75(1):119~125
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