Diffeomorphisms of 4-manifolds from graspers
Danica Kosanovi\'c

TL;DR
This paper explores how degree one grasper families of embedded circles relate to various known constructions of diffeomorphisms in 4-manifolds, using a parameterised surgery map to connect embeddings to the mapping class group.
Contribution
It introduces a unified framework linking different diffeomorphism constructions via graspers and a parameterised surgery map in 4-manifold topology.
Findings
Establishes connections between graspers and theta clasper classes.
Relates barbell diffeomorphisms to graspers.
Provides a new perspective on twin twists through graspers.
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 takes loops of framed embeddings of in the manifold obtained by surgery on some 2-sphere in , to the mapping class group of .
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Taxonomy
TopicsGeometric and Algebraic Topology · Control and Dynamics of Mobile Robots · Robotic Mechanisms and Dynamics
