Smooth unknotting conjecture in dimension four and search for essence of mathematics

必要的和。蚂蚁解结的条件是众所周知的，除了平滑的2个结。补码具有相同的同伦型，条件是平凡的纽结。我们的目的是证明这个条件对于剩下的情况也是足够的，使用二维辫子理论这个方法是相当初级的，我们想在这个机会中找到一些数学的本质。1)我们已经有了一个单参数映射族，在给定的条件下的纽结和平凡的纽结之间只有尖点出生和死亡。2)通过推广Kamada的方法，将其转化为单参数奇异2-辫子簇。3)如有必要，通过应用稳定化来找到其图表描述。4)交点的高度可以向下修改，直到水平略高于相关的尖点消亡。5)将问题简化为交点个数为1，通过旋转图中其他固定顶点使交点向下移动，然后在顶点消失的情况。6)根据Kamada-MatSumoto的单词表示，这一步骤可以分为几个简单的步骤。7)每一步都会显示其末端是平凡的二维辫子。这是一个解决猜想的提纲。至于数学的本质，除了每个研究者的研究之外，我们还研究了高津关死300年后的行列式的历史。

The necessary and. ant condition for unknotting is well-known except for a smooth 2-knot. The complement has the same homotopy type with a trivial knot is the condition. Our aim is to show that this condition is enough also for the remaining case, using 2-dimensional braid theory The method is quite elementary and we want to find some essence of mathematics in this chance.1) We have already a one-parameter family of maps with only cusp births and deaths between a given knot with the condition and a trivial knot. 2) Transform this to a one-parameter family of singular 2-braids by extending a method due to Kamada. 3) Find its chart description by applying stabilization if necessary. 4) The height of an intersection point can be modified down until the level a little higher than the related cusp death. 5) This reduces the problem to the case that the number of intersection points is one and the intersection point go down by rotating the other fixed vertices of the chart and then disappear at the cusp. 6) This step can be divided into several simple steps by a word representation due to Kamada-Matsumoto. 7) Each step will be shown that the ends are turned out to be trivial 2-dimensional braids. This is an outline to solve the conjecture.As for essence of mathematics besides the study by each investigator we studied the history of determinants at the occasion of 300 years after the death of Takakazu Seki.