发表机构
Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究确定了同调中无2-挠和3-挠的单连通闭自旋5维流形的Torelli群与配边群的同构关系，明确了#^g(S²×S³)的映射类群及其相关代数性质，还研究了S³在S²×S³中的嵌入。
AI 中文摘要
我们证明：单连通闭5维流形M的Torelli群（M为自旋流形且同调中无2-挠元）配边群Ω^Spin_6(K(H₂(M),2))是同构的。对H₂(M)无2-挠和3-挠的情况，我们确定了该配边群，并给出了Torelli群生成元的显式构造。此外，对g重连通和#^g(S²×S³)，我们完全确定了其映射类群。我们应用所得结果计算#^g(S²×S³)的映射类群的稳定化与阿贝尔化，确定与M同伦等价的M的微分同胚的同痕类群，并研究S³在S²×S³中的嵌入。
英文摘要
We show that the Torelli group of a simply connected closed 5-manifold $M$, which is spin and has no 2-torsion elements in homology, is isomorphic to the bordism group $Ω^{\mathrm{Spin}}_6(K(H_2(M), 2))$. For $H_2(M)$ with no 2- and 3-torsion we determine this bordism group, and give explicit constructions for the generators of the Torelli group. Furthermore, for the $g$-fold connected sum ${\#}^g(S^2 \times S^3)$ we completely determine its mapping class group. We apply our results to compute the stabilization and abelianization of the mapping class group of ${\#}^g(S^2 \times S^3)$, determine the group of isotopy classes of diffeomorphisms of $M$ that are homotopic to the identity, and study the embeddings of $S^3$ in $S^2 \times S^3$.
Comments47 pages. Comments welcome
