论文标题
在cantor灰尘上的组合整合
A combinatorial integration on the Cantor dust
论文作者
论文摘要
在本文中，我们将Cantor功能推广到$ 2 $维的立方体，并在Cantor Dust上构建一个环状$ 2 $ cocycle。该旋子在$ 2 $维的圆环上的平滑功能的回调上是无处不在的，具有广义的cantor函数，而它在cantor灰尘上的Lipschitz函数上消失了。通过使用组合Fredholm模块，通过在圆环上的$ 2 $形式的集成来计算合子。
In this paper, we generalize the Cantor function to $2$-dimensional cubes and construct a cyclic $2$-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the $2$-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of $2$-forms on the torus by using a combinatorial Fredholm module.
