Mapping class group of a surface is generated by two elements

Wajnryb, Bronislaw

doi:10.1016/0040-9383(95)00037-2

Cited by 44 publications

(30 citation statements)

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“…We also prove that the extended mapping class group Mod * g,1 is generated by two elements, again one of which is a Dehn twist. Our proofs are independent from that of Wajnryb [8]. Next, we prove that the mapping class groups Mod g,1 and Mod g are also generated by two torsion elements.…”

Section: Introductionmentioning

confidence: 99%

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Generating the surface mapping class group by two elements

Korkmaz

2004

Trans. Amer. Math. Soc.

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Abstract. Wajnryb proved in 1996 that the mapping class group of an orientable surface is generated by two elements. We prove that one of these generators can be taken as a Dehn twist. We also prove that the extended mapping class group is generated by two elements, again one of which is a Dehn twist. Another result we prove is that the mapping class groups are also generated by two elements of finite order.

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Section: Introductionmentioning

confidence: 99%

“…, a 2g on Σ also generate Mod 1 g . Finally, the minimal number of generators for the mapping class group is determined by Wajnryb [8]. He showed that Mod 1 g , and hence Mod g , can be generated by two elements; one is a product of two Dehn twists (one is right and one is left) and the other is a product of 2g Dehn twists.…”

Section: Introductionmentioning

confidence: 99%

Generating the surface mapping class group by two elements

Korkmaz

2004

Trans. Amer. Math. Soc.

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“…The calculation of G:H for a compact Calabi-Yau space is an interesting and challenging problem. By analogy with the mapping class group of a genus-g Riemann surface [18], we may expect that G:H is finite. In fact, the monodromy group H can be generated by two elements, which correspond to monodromies around the conifold point and infinity.…”

Section: Conclusion and Further Issuesmentioning

confidence: 99%

Entropic principle and asymptotic freedom

2006

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Motivated by the recent developments about the Hartle-Hawking wave function associated to black holes, we formulate an entropy functional on the moduli space of Calabi-Yau compactifications. We find that the maximization of the entropy is correlated with the appearance of asymptotic freedom in the effective field theory. The points where the entropy is maximized correspond to points on the moduli which are maximal intersection points of walls of marginal stability for Bogomolnyi-Prasad-Sommerfield states. We also find an intriguing link between extremizing the entropy functional and the points on the moduli space of Calabi-Yau three folds which admit a ''quantum deformed'' complex multiplication.

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“…Geometric properties of M played a crucial role in the problem of finding particular sets of generators for M g and M ± g cf. [3,7,8,11]. Following [1], let t 1 , s 1 , .…”

Section: Preliminariesmentioning

confidence: 99%

“…It is known that this set of generators of M g is not minimal, and a great deal of attention has been paid to the problem of finding a minimal (or at least small) set of generators or a set of generators with some additional property. For different approaches to this problem see [3,5,7,8,10,11] and references there. The main purpose of this note is to prove that for g ≥ 1 the extended mapping class group M ± g is generated by three symmetries, i.e.…”

Section: Introductionmentioning

confidence: 99%