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A computation of H1(Γ, H1(Σ))

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  • Rasmus Villemoes, Denmark

Let Σ = Σg,1 be a compact surface of genus g at least 3 with one boundary component, Γ its mapping class group and M = H1(Σ, ℤ) the first integral homology of Σ. Using that Γ is generated by the Dehn twists in a collection of 2g+1 simple closed curves (Humphries' generators) and simple relations between these twists, we prove that H1(Γ, M) is either trivial or isomorphic to ℤ. Using Wajnryb's presentation for Γ in terms of the Humphries generators we can show that it is not trivial.

Original languageEnglish
PublisherarXiv.org
Number of pages9
Publication statusPublished - 23 Feb 2011

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