The Goeritz groups of (1,1)-decompositions
arxiv(2024)
摘要
A (g, n)-decomposition of a link L in a closed orientable 3-manifold
M is a decomposition of M by a closed orientable surface of genus g into
two handebodies each of which intersects the link L in n trivial arcs. The
Goeritz group of that decomposition is then defined to be the group of isotopy
classes of orientation-preserving homeomorphisms of the pair (M, L)
preserving the decomposition. We compute the Goeritz groups of all
(1,1)-decompositions.
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