 Semidirect-product decomposition of the pure mapping class group of the five-punctured sphere

ID: semidirect-product-decomposition-of-the-pure-mapping-class-group-of-the-five-punctured-sphere

Forgetting the fifth puncture gives a split Birman exact sequence

1 \to F_{3} \to PMod (S_{0, 5}) \to F_{2} \to 1.

Lifts of two free generators generate a copy of

F_{2}

meeting the point-pushing kernel

F_{3}

trivially.

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