Nontangential homotopy equivalences

Victor Allen Belfi

Vol. 36 (1971), No. 3, 615–621

DOI: 10.2140/pjm.1971.36.615

Abstract

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 N^4k 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 {M_t} satisfying (1) no M_i is a π− manifold, (2) each M_i is homotopy equivalent but not homeomorphic to N ×L, (3) M_t is not homeomorphic to M_j if i≠j.

Mathematical Subject Classification

Primary: 57.31

Milestones

Received: 3 October 1969

Revised: 9 June 1970

Published: 1 March 1971