论文标题
数字拓扑中的lefschetz数字和固定点理论
Lefschetz numbers and fixed point theory in digital topology
论文作者
论文摘要
在本文中，我们在数字图像拓扑中介绍了两种类型的lefschetz数字。也就是说，Simplicial Lefschetz编号$ L（F）$和Cubical Lefschetz编号$ \ bar l（f）$。我们表明$ l（f）$是一个强大的同型不变性，并且具有近似的固定点定理。另一方面，我们确定$ \ bar l（f）$是同质的不变性，并且具有$ n $ app的固定点结果。从本质上讲，这意味着$ l（f）$的固定点结果比$ \ bar l（f）$要好，而$ \ bar l（f）$的同质副本不变性优于$ l（f）$。与经典拓扑不同，这些Lefschetz数字为近似固定点的数量提供了下限。最后，我们构建了一些说明性的例子来证明我们的结果。
In this paper, we present two types of Lefschetz numbers in the topology of digital images. Namely, the simplicial Lefschetz number $L(f)$ and the cubical Lefschetz number $\bar L(f)$. We show that $L(f)$ is a strong homotopy invariant and has an approximate fixed point theorem. On the other hand, we establish that $\bar L(f)$ is a homotopy invariant and has an $n$-approximate fixed point result. In essence, this means that the fixed point result for $L(f)$ is better than that for $\bar L(f)$ while the homotopy invariance of $\bar L(f)$ is better than that of $L(f)$. Unlike in classical topology, these Lefschetz numbers give lower bounds for the number of approximate fixed points. Finally, we construct some illustrative examples to demonstrate our results.
