论文标题
同源性琐事的广义Harer猜想
The generalized Harer conjecture for the homology triviality
论文作者
论文摘要
经典的Harer猜想是关于明显嵌入$ ϕ的稳定同源性微不足道的：b_ {2g+2} \hookrightarrowγ_{g} $，这是Song and Tillmann证明的。证明的主要部分是证明$ \ bϕ^{+}：\ b b b _ {\ infty}^{+} \ rightArrow \ rightArrow \bγ_{\ infty}^{+}^{+} $是从$ ϕ $诱导的。在本文中，我们给出了广义Harer猜想的证明，该猜想是关于$ nutivary $嵌入$ ϕ的同源性琐事的证明：b_ {n} \jookegrightarrowγ__{g，k} $。我们首先表明，对于$常规$嵌入，所有原子表面都被认为是相同的，并且每个原子扭曲都是一个{\ IT简单的twist}互换了两个原子表面的两个相同的子零件。证据的主要策略是证明$ \ rightarrow \ Mathcal \ rightArrow \ Mathcal {s} $由$ \ bx引起的：\ conf_n（d）\ rightarrow \ rightArrow \ rightArrow \ rightarrow {m} _ {m} _ {g，k，k，k} $保留了所构成的小2 d-disks bilter dib hild 2-disp的动作。
The classical Harer conjecture is about the stable homology triviality of the obvious embedding $ϕ: B_{2g+2} \hookrightarrow Γ_{g}$, which was proved by Song and Tillmann. The main part of the proof is to show that $\Bϕ^{+} : \B B_{\infty}^{+} \rightarrow \B Γ_{\infty}^{+}$ induced from $ϕ$ 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 $ϕ: B_{n} \hookrightarrow Γ_{g,k}$. 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 $Φ: \mathcal{C} \rightarrow \mathcal{S}$ induced by $\Bϕ:\conf_n(D)\rightarrow\mathcal{M}_{g,k}$ preserves the actions of the framed little 2-disks operad.
