A simple class of infinitely many absolutely exotic manifolds

2018/03/08 by Selman Akbulut, Akbulut, Selman
Mathematics · #57R65 #58A05 #58D27 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1803.03256

openalex publication_date 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the smooth 4-manifold M obtained by attaching a 2-handle to B⁴ along a certain knot K⊂ ∂ B⁴ admits infinitely many absolutely exotic copies M_n, n=0,1,2.., such that each copy M_n is obtained by attaching 2-handle to a fixed compact smooth contractible manifold W along the iterates fⁿ(c) of a knot c⊂ ∂ W by a diffeomorphism f:∂ W → ∂ W. This generalizes the example in author's 1991 paper, which corresponds to n=1 case.

Related

• On absolutely exotic diffeomorphisms of 4-manifolds
• Absolutely exotic compact 4-manifolds
• Corks, exotic 4-manifolds and genus functions
• Construction of Exotic Smooth Structures
• Traces of links and simply connected 4-manifolds