论文标题
从某些两种复合物的强烈溢流图上有微不足道的顶级杂种学到投影平面
Strongly surjective maps from certain two-complexes with trivial top-cohomology onto the projective plane
论文作者
论文摘要
For the model two-complex $K$ of the group presentation $\mathcal{P}=\langle x,y\,|\,x^{k+1}yxy \rangle$, with $k\geq1$ odd, we describe representatives for all free and based homotopy classes of maps from $K$ into the real projective plane and we classify the homotopy classes containing only surjective maps.通过这种方法，我们得到了一个答案，用于将图像映射到真实的投影平面，对于拓扑根理论中的一个经典问题，到目前为止，在第二个维度上已经知道，仅适用于球体，圆环和klein瓶的地图。答案得出的是证明所有$ k \ geq1 $奇数，$ h^2（k; mathbb {z}）= 0 $，对于$ k \ geq3 $奇数，从$ k $ ods中存在从$ k $到真正的投射平面，这些平面是强烈露面的。对于$ k = 1 $，没有如此强烈的溢出地图。 55N25，57M20。
For the model two-complex $K$ of the group presentation $\mathcal{P}=\langle x,y\,|\,x^{k+1}yxy \rangle$, with $k\geq1$ odd, we describe representatives for all free and based homotopy classes of maps from $K$ into the real projective plane and we classify the homotopy classes containing only surjective maps. With this approach we get an answer, for maps into the real projective plane, for a classical question in topological root theory, which is known so far, in dimension two, only for maps into the sphere, the torus and the Klein bottle. The answer follows by proving that for all $k\geq1$ odd, $H^2(K;mathbb{Z})=0$ and, for $k\geq3$ odd, there exist maps from $K$ into the real projective plane which are strongly surjective. For $k=1$, there is no such a strongly surjective map. 55N25, 57M20.
