Vol. 36, No. 3, 1971

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Nontangential homotopy equivalences

Victor Allen Belfi

Vol. 36 (1971), No. 3, 615–621

The purpose of this paper is to apply surgery techniques in a simple, geometric way to construct manifolds which are nontangentially homotopy equivalent to certain π-manifolds. Applying this construction to an H-manifold of the appropriate type yields an infinite collection of mutually nonhomeomorphic H-manifolds, all nontangentially homotopy equivalent to the given one.

The theorem proved is the following: If N4k is a smooth, closed, orientable π-manifold and Ln is a smooth, closed, simply connected π-manifold, there is a countable collection of smooth, closed manifolds {Mt} satisfying (1) no Mi is a π manifold, (2) each Mi is homotopy equivalent but not homeomorphic to N ×L, (3) Mt is not homeomorphic to Mj if ij.

Mathematical Subject Classification
Primary: 57.31
Received: 3 October 1969
Revised: 9 June 1970
Published: 1 March 1971
Victor Allen Belfi