2025/05/29 by Shital Lawande, Lawande, Shital, Kuldeep Saha +1
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2505.23999
We give an example of a smooth characteristic embedding of a torus in \s2 × \s2 # \s1 × \s3 such that there exists no diffeomorphism of the ambient 4-manifold that induces the Dehn twist along a meridian of the torus, but there exists a homeomorphism of the ambient 4-manifold, isotopic to identity, that induces the Dehn twist. As an application of our methods, we provide examples of two proper smooth embeddings of an annulus in \s2 × \s2 # \s1 × \s3 ∖ int(\D4) which are topologically isotopic, but not smoothly isotopic (relative to boundary).