Sphere recognition is known to be undecidable in dimensions five and beyond, and no polynomial time method is known in dimensions three and four. Here we report on positive and negative computational results with the goal to explore the limits of sphere recognition from a practical point of view. An important ingredient are randomly constructed discrete Morse functions.

翻译：众所周知,在五维及以后的维度中,球体的识别是不可分的,在三维和四维中,并不存在多元时间方法。在这里,我们报告正负计算结果,目的是从实际角度探索球体识别的限度。一个重要成份是随机构造的离散摩斯函数。