Quasi-homomorphisms on mapping class groups vanishing on a handlebody group

Jiming Ma; Jiajun Wang

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arXiv · 1907.03290

Quasi-homomorphisms on mapping class groups vanishing on a handlebody group

Jiming Ma·Jiajun Wang

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Abstract

We construct infinitely many linearly independent quasi-homomorphisms on the mapping class group of a Riemann surface with genus at least two which vanish on a handlebody subgroup. As a corollary, we disprove a conjecture of Reznikov on bounded width in Heegaard splittings. Another corollary is that there are infinitely many linearly independent quasi-invariants on the Heegaard splittings of three-manifolds.

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Jiming Ma, Jiajun Wang. 2019-07-07. Quasi-homomorphisms on mapping class groups vanishing on a handlebody group. https://arxiv.org/abs/1907.03290

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