First cohomology of pure mapping class groups of big genus one and zero surfaces

George Domat; Paul Plummer

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arXiv · 1904.10565

First cohomology of pure mapping class groups of big genus one and zero surfaces

George Domat·Paul Plummer

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Abstract

We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphism to $\mathbb{Z}$ factors through a sphere with finitely many punctures. In fact we get an uncountable family of such maps.

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George Domat, Paul Plummer. 2019-04-23. First cohomology of pure mapping class groups of big genus one and zero surfaces. https://arxiv.org/abs/1904.10565

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