Vol. 42, No. 3, 1972

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Boundary respecting maps of 3-mainfolds

Benny Dan Evans

Vol. 42 (1972), No. 3, 639–655

This paper is about maps of compact 3-manifolds which map the boundary of the domain (possibly nonhomeomorphically) into the boundary of the range. F. Waldhausen has shown that such a map between compact, orientable, irreducible S-manifolds with nonempty, incompressible boundary is homotopic to a homeomorphism if and only if the map induces an isomorphism at the fundamental group level. The main theorem of this paper states that the above theorem remains valid if the assumption of incompressible boundary is dropped. A study of disk sums of bounded 3-manifolds will be required in order to prove the above-mentioned theorem. This investigation involves theorems about disk sums of bounded 3-manifolds analogous to the classical Kneser theorem for closed 3-manifolds.

Mathematical Subject Classification
Primary: 57A10
Received: 27 May 1971
Revised: 25 January 1972
Published: 1 September 1972
Benny Dan Evans