2010/11/24 by Motoo Tange, Tange, Motoo
Mathematics · #57M25 #57R50 #57R65 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1011.5308
openalex publication_date 2010/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fintushel-Stern's knot surgery gave many pairs of exotic manifolds, which are homeomorphic but non-diffeomorphic. We show that if an elliptic fibration has two parallel, oppositely oriented vanishing circles (for example S2× S2 or Matsumoto's S4), then the knot surgery gives rise to standard manifolds. The diffeomorphism can give an alternative proof that Scharlemann's manifold is standard (originally by Akbulut [Ak1]).