Mathematical Sciences: Topological Rigidity

F. Thomas Farrell与l.e. Jones（来自纽约州立大学石溪分校）合作，希望在紧流形M的基群为矩阵群且M的维数大于4的情况下，使外科理论成为计算紧流形M的同伦拓扑结构集的合理方法。（对基本群的更强的约束可能是必要的，例如，它是无扭转的，并且是在有理数上定义的半简单代数群的算术子群。）第二个（也是相关的）问题是使瓦尔德豪森的工作成为合理计算方法的基础。

F. Thomas Farrell, in collaboration with L. E. Jones (of S.U.N.Y. at Stony Brook), hopes to make surgery theory a reasonable method for calculating the homotopy-topological structure set of a compact manifold M provided its fundamental group is a matrix group and the dimension of M is greater than 4. (Stronger constraints on the fundamental group may be necessary; e.g., that it is torsion-free and is an arithmetic subgroup of a semi-simple algebraic group defined over the rationals.) A second (and related) problem is to make Waldhausen's work the basis of a reasonable method for calculating.