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- W4283707329 abstract "The classical Harer conjecture is about the stable homology triviality of the obvious embedding $phi : B_{2g+2} hookrightarrow Gamma_{g}$, which was proved by Song and Tillmann. The main part of the proof is to show that $Bphi^{+} : B B_{infty}^{+} rightarrow B Gamma_{infty}^{+}$ induced from $phi$ is a double loop space map. In this paper, we give a proof of the generalized Harer conjecture which is about the homology triviality for an $arbitrary$ embedding $phi : B_{n} hookrightarrow Gamma_{g,k}$. We first show that it suffices to prove it for a $regular$ embedding in which all atomic surfaces are regarded as identical and each atomic twist is a {it simple twist} interchanging two identical sub-parts of atomic surfaces. The main strategy of the proof is to show that the map $Phi : mathcal{C} rightarrow mathcal{S}$ induced by $Bphi:conf_n(D)rightarrowmathcal{M}_{g,k}$ preserves the actions of the framed little 2-disks operad." @default.
- W4283707329 created "2022-06-30" @default.
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- W4283707329 date "2022-06-27" @default.
- W4283707329 modified "2023-10-15" @default.
- W4283707329 title "The generalized Harer conjecture for the homology triviality" @default.
- W4283707329 doi "https://doi.org/10.48550/arxiv.2206.13333" @default.
- W4283707329 hasPublicationYear "2022" @default.
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