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Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 4

Number of pseudo–Anosov elements in the mapping class group of a four–holed sphere

Ferihe ATALAN
Mustafa KORKMAZ
Pages
585–592
Publication Date
2022-11-03
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set.
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Key Findings & Data:We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set.
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Conclusion & Impact:We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.

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Cite This Article

ATALAN, F., KORKMAZ, M. (2022). Number of pseudo–Anosov elements in the mapping class group of a four–holed sphere. Turkish Journal of Mathematics, Cilt: 34 - Sayı: 4, 585–592. https://ajindex.com/articles/608514

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References (7)

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