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- W3097799163 abstract "For $$g>3$$ , we give two proofs of the fact that the Birman exact sequence for the Torelli group $$begin{aligned} 1rightarrow pi _1(S_g)rightarrow {mathcal I}_{g,1}rightarrow {mathcal I}_grightarrow 1 end{aligned}$$ does not split. This result was claimed by Mess (Unit tangent bundle subgroups of the mapping class groups, MSRI Pre-print, 1990), but his proof has a critical and unrepairable error which will be discussed in the introduction. Let $${mathcal Umathcal I}_{g,n}xrightarrow {Tu'_{g,n}} {mathcal B} {mathcal I}_{g,n}$$ (resp. $${mathcal U}{mathcal P}{mathcal I}_{g,n}xrightarrow {Tu_{g,n}}{mathcal B}{mathcal P}{mathcal I}_{g,n}$$ ) denote the universal surface bundle over the Torelli space fixing n points as a set (resp. pointwise). We also deduce that $$Tu'_{g,n}$$ has no sections when $$n>1$$ and that $$Tu_{g,n}$$ has precisely n distinct sections for $$nge 0$$ up to homotopy." @default.
- W3097799163 created "2020-11-09" @default.
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- W3097799163 date "2020-10-27" @default.
- W3097799163 modified "2023-09-26" @default.
- W3097799163 title "The universal surface bundle over the Torelli space has no sections" @default.
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- W3097799163 doi "https://doi.org/10.1007/s00209-020-02625-2" @default.
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