2022/06/28 by Daniel Kasprowski, Mark Powell, Kasprowski, Daniel +3
Computer Science · Mathematics · #57K40 #57N70 #57R80 #Data Management and Algorithms #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2206.14113
openalex publication_date 2022/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a compact 4-manifold and let S and T be embedded 2-spheres in M, both with trivial normal bundle. We write MS and MT for the 4-manifolds obtained by the Gluck twist operation on M along S and T respectively. We show that if S and T are concordant, then MS and MT are s-cobordant, and so if π1(M) is good, then MS and MT are homeomorphic. Similarly, if S and T are homotopic then we show that MS and MT are simple homotopy equivalent. Under some further assumptions, we deduce that MS and MT are homeomorphic. We show that additional assumptions are necessary by giving an example where S and T are homotopic but MS and MT are not homeomorphic. We also give an example where S and T are homotopic and MS and MT are homeomorphic but not diffeomorphic.