论文标题
Riemann表面的同源组自动形态
Homology group automorphisms of Riemann surfaces
论文作者
论文摘要
如果$γ$是一个有限生成的紫红色群体，以致其派生的亚组$γ'$是无共同的，则是免费的，那么$ s = {\ mathbb h}^{2}^{2}/γ'$是封闭的riemann riemann riemann $ g \ g \ geq 2 $ abelian Glops $ a abelian $ a $ a =γ/γ/γ''=γ/γ''我们说$ a $是$ s $的同源组。一个自然的问题是，$ s $是否接受独特的同源群，换句话说，是否有不同的fuchsian组$γ_{1} $和$γ_{2} $，with $γ_{1}'=γ'_ _ {2} $？ It is known that if $Γ_{1}$ and $Γ_{2}$ are both of the same signature $(0;k,\ldots,k)$, for some $k \geq 2$, then the equality $Γ_{1}'=Γ_{2}'$ ensures that $Γ_{1}=Γ_{2}$.概括这一点，我们观察到，如果$γ_{j} $具有签名$（0; k_ {j}，\ ldots，k_ {j}）$和$γ_{1}'=γ'_ _ {2} $，则$γ_{1} =γ_{2} $ {2} $。我们还提供与不同同源组的表面$ s $的示例。还获得了每个同源组$ a $的$ {\ rm aut}（s）$中的标准式描述。
If $Γ$ is a finitely generated Fuchsian group such that its derived subgroup $Γ'$ is co-compact and torsion free, then $S={\mathbb H}^{2}/Γ'$ is a closed Riemann surface of genus $g \geq 2$ admitting the abelian group $A=Γ/Γ'$ as a group of conformal automorphisms. We say that $A$ is a homology group of $S$. A natural question is if $S$ admits unique homology groups or not, in other words, is there are different Fuchsian groups $Γ_{1}$ and $Γ_{2}$ with $Γ_{1}'=Γ'_{2}$? It is known that if $Γ_{1}$ and $Γ_{2}$ are both of the same signature $(0;k,\ldots,k)$, for some $k \geq 2$, then the equality $Γ_{1}'=Γ_{2}'$ ensures that $Γ_{1}=Γ_{2}$. Generalizing this, we observe that if $Γ_{j}$ has signature $(0;k_{j},\ldots,k_{j})$ and $Γ_{1}'=Γ'_{2}$, then $Γ_{1}=Γ_{2}$. We also provide examples of surfaces $S$ with different homology groups. A description of the normalizer in ${\rm Aut}(S)$ of each homology group $A$ is also obtained.
