A Note on Some Contractible 4-Manifolds

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

[1]  M. Newman,et al.  Boundaries of ULC Sets in Euclidean n-Space. , 1948, Proceedings of the National Academy of Sciences of the United States of America.

[2]  J. Whitehead.  Simplicial Spaces, Nuclei and m‐Groups , 1939 .

[3]  J. Whitehead.  On Involutions of Spheres , 1957 .

[4]  Morton Brown,et al.  A proof of the generalized Schoenflies theorem , 1960 .