A recipe for exotic 2-links in closed 4-manifolds whose components are topological unknots

2022/06/20 by Bais, Valentina, Younes Benyahia, Benyahia, Younes +4
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2206.09659

openalex publication_date 2022/06/20 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

Abstract

We describe a construction procedure of infinite sets of 2-links in closed simply connected 4-manifolds that are topologically isotopic, smoothly inequivalent and componentwise topologically unknotted. These 2-links are the first examples of such kind in the literature. The examples provided have surface and free groups as their 2-link groups. We also point out an exotic Brunnian behaviour of such families, which highlights the important role of linking in creating exotic phenomena.

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