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Equisingularity at the critical set versus topological equisingularity
Conjecture A. The family $f_t$ is equisingular at the critical set if and only if $f_t$ is topologically equisingular to $f_{t'}$ for any parameters $t,t'$ .
Conjectureopenequisingularity function-germs singularity-theoryarXiv posted 2 days ago

Equisingularity at the critical set versus topological equisingularity