Mathematical Sciences: Topological Rigidity

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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.