Vol. 36, No. 3, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
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