New Homotopy 4-Spheres

2011/01/15 by Daniel Nash, Nash, Daniel
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1101.2981

openalex publication_date 2011/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S⁴ and hence homeomorphic to S⁴ but possibly not diffeomorphic to S⁴). It is still unknown if these new examples are in fact exotic.

Citations

• Cappell-Shaneson homotopy spheres are standard

Related

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• A novel construction of homotopy 4-spheres and real projective 4-spaces à la Cappell-Shaneson
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• Cappell-Shaneson homotopy spheres are standard
• Some examples of aspherical 4-manifolds that are homology 4-spheres