论文标题
Borsuk-ulam定理3个manifolds
The Borsuk-Ulam theorem for 3-manifolds
论文作者
论文摘要
我们研究三重（M;τ; \ r^n）的Borsuk-ulam定理，其中M是一个紧凑的，连接的，配备了无固定点的相关性τ。 Borsuk-ulam定理所持的n的最大价值称为Z_2索引，在我们的情况下，它具有1、2或3的值。我们根据应用于h^1（n; Z_2）中特征类X \的共生学操作进行了完全讨论该指数，其中n = m/°= m/°τisorbit空间。在定向的情况下，我们从轨道空间的手术表现的链接基质中获得了指数的表达。我们用示例包括不可定位的结果来说明我们的结果。
We study the Borsuk-Ulam theorem for triple (M;τ; \R^n), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution τ. The largest value of n for which the Borsuk-Ulam theorem holds is called the Z_2-index and in our case it takes value 1, 2 or 3. We fully discuss this index according to cohomological operations applied on the characteristic class x \in H^1(N; Z_2), where N = M/τis the orbit space. In oriented case, we obtain an expression of the index from the linking matrix of a surgery presentation of the orbit space. We illustrate our results with examples, including a non orientable one.
