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A Note on Some Contractible 4-Manifolds

Barry Mazur

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Abstract

In a recent note [2], J. H. C. Whitehead exhibits involutions of Sn with fixed point sets non-simply connected, for n > 14. This is based on a certain example of M.H.A. Newman [1] of a contractible 5-manifold U5, with non-simply connected boundary. The purpose of this note is to construct specific 4-manifolds W4 which are contractible and have nonsimply connected boundaries & W, = Mr (which are necessarily homology 3-spheres), and which have the following additional property

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What this paper is about

In a recent note [2], J. H. C. Whitehead exhibits involutions of Sn with fixed point sets non-simply connected, for n > 14. This is based on a certain example of M.H.A. Newman [1] of a contractible 5-manifold U5, with non-simply connected boundary. The purpose of this note is to construct specific 4-manifolds W4 which are contractible and have nonsimply connected boundaries & W, = Mr (which are necessarily homology 3-spheres), and which have the following additional property

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Available abstract

In a recent note [2], J. H. C. Whitehead exhibits involutions of Sn with fixed point sets non-simply connected, for n > 14. This is based on a certain example of M.H.A. Newman [1] of a contractible 5-manifold U5, with non-simply connected boundary. The purpose of this note is to construct specific 4-manifolds W4 which are contractible and have nonsimply connected boundaries & W, = Mr (which are necessarily homology 3-spheres), and which have the following additional property

Key concepts: Contractible space, Mathematics, Pure mathematics, Combinatorics

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