Celebratio Mathematica — Rourke — Complete Bibliography

Complete Bibliography

Works connected to Eugénia César de Sá

Filter the Bibliography List

year	title	people

			clear

E. César de Sá and C. Rourke: “The homotopy type of homeomorphisms of 3-manifolds,” Bull. Am. Math. Soc., New Ser. 1 (1979), pp. 251–254. MR 513752 Zbl 0442.58007 article

The purpose of this paper is to announce some results on homeomorphism groups of 3-manifolds. These results together with the Smale conjecture (a proof of which has recently been announced by A. Hatcher) essentially reduce the com- putation of the homotopy type of the homeomorphism group of a 3-manifold to an analysis of a certain associated configuration space and the homotopy types of the homeomorphism groups of the prime factors. For a prime 3-manifold, this homotopy type is known (a) if the manifold is \( P^2 \)-irreducible and sufficiently large, (b) for \( S^1 \times S^2 \) and \( S^1 \underset{\sim}{\times} S^2 \).

The results announced here are an extension of the first part of the first author’s Ph.D. thesis and use the methods of this thesis. None of our results depends on the Smale conjecture but we have indicated where the Smale conjecture simplifies the conclusion.