Applications of centers of mass configuration spaces to homotopy theory

同伦理论是研究两个空间间连续映射的一种拓扑学。传统上，同伦理论中的问题都是用特别的方法来解决的。在本研究中，我定义了“质心”构形空间，并对其性质提出了一个猜想。我阐明，如果我们的猜想被证明，那么不仅许多已知的结果被完整地否定了，而且我们也可以证明未解决的问题。本研究的优点如下。欧氏空间中超平面的补是一个可计算的对象。由于我们的构形空间是一种这样的补充，我们的猜想比构造连续映射的传统方法更容易理解。

Homotopy theory is a topology which studies continuous maps between two spaces. Traditionally, problems in homotopy theory have been solved by ad hoc methods. In the present research, I defined the "centers of mass" configuration spaces and posed a conjecture about its property. I elucidated that if our conjecture was proved, then not only many known results are reproved in an integral way, but also we can prove unsolved problems.The merit of our research is as follows. The complement of hyperplanes in the Euclidean space is a computable object. Since our configuration space is a kind of such a complement, our conjecture is far more accessible than the traditional way to construct continuous maps.