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Divides with cusps and symmetric links
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abstract
A Divide with cusps is the image of a proper generic immersion from finite intervals and circles into a $2$-disk which allows to have cusps. A divide with cusps is the generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in $S^3$. In this paper, we give the characterization of the link in $S^3$ which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and $2$-periodic link can be described as the link of a divide with cusps.
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Cited by 1 Pith paper
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Real morsifications via the trace map
Every reduced real plane curve singularity is shown to admit a real morsification, via a new trace map built from nodal smoothings of normalization disks.
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