New Homotopy 4-Spheres

Abstract

We use surgery along 2-tori embedded in a union of two copies of a product of punctured 2-tori to produce a new collection of homotopy 4-spheres (4-manifolds homotopy equivalent to $S^4$ and hence homeomorphic to $S^4$ but possibly not diffeomorphic to $S^4$). It is still unknown if these new examples are in fact exotic.

11 pages, 5 figures

References in corpus (1)

• Cappell-Shaneson homotopy spheres are standard

Cited by in corpus (1)

• Nash homotopy spheres are standard