Diffeomorphisms of 4-manifolds from graspers

2024/05/09 by Danica Kosanović, Kosanović, Danica
Engineering · Mathematics · #57K40 #57K45 #57R40 #57R50 #57S05 #Control and Dynamics of Mobile Robots #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2405.05822

openalex publication_date 2024/05/09 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28

Abstract

We relate degree one grasper families of embedded circles to various constructions of diffeomorphisms found in the literature -- theta clasper classes of Watanabe, barbell diffeomorphisms of Budney and Gabai, and twin twists of Gay and Hartman. We use a ``parameterised surgery map'' that for a smooth 4-manifold M takes loops of framed embeddings of S¹ in the manifold obtained by surgery on some 2-sphere in M, to the mapping class group of M.

Related

• Diffeomorphisms of the 4-sphere, Cerf theory and Montesinos twins
• 4-manifolds, surgery on loops and geometric realization of Tietze\n transformations
• Grasper families of spheres in S² × D² and barbell diffeomorphisms of S¹× S² × I
• Knotted families from graspers
• Stable classification of 4-manifolds obtained by the surgery on loops