Mathematical Sciences: Cohomological Dimension

这项研究集中在维度理论的代数方面。该项目的关键部分是确定欧几里得4-空间的细胞状图像是否是有限维的。证明(或反驳)上同调维度理论中类似于覆盖维度理论中的结果是该项目的另一个目标。对于除4维以外的欧几里得空间，关键问题的类似问题的答案是已知的。这是拓扑问题的难度不随维度增加的另一种情况。令人痛心的是，最大的谜团与我们生活的三维空间或四维空间有关，这可能被视为时空。

This research concentrates on algebraic aspects of dimension theory. The crucial part of the project is to decide whether cell- like images of euclidean 4-space are finite-dimensional. Proving (or disproving) results in cohomological dimension theory which are analogous to results in covering dimension theory is another goal of the project. The answers are known to the analogues of the key question for Euclidean spaces of dimensions other than 4. This is another case where the difficulty of a topological question does not increase with dimension. It is distressing to find that the greatest mysteries concern the space of three dimensions in which we live or the space of four dimensions, which may be viewed as space-time.