7 problems

Conjecture C. $f$ is a function germ with smooth $1$-dimensional critical set such that the transversal Milnor number of $f$ at every point of its critical set is equal to $\mu$.

Conjecture B. Any function germ $g$ topologically equisingular to $f$ has smooth critical set and constant transversal Milnor number.

Let $(V,0)$ be a hypersurface surface singularity, and let its Milnor fibre carry its intersection form with signature defined in the usual way. Durfee's conjecture. The signature…

Bouquet conjecture. The Milnor fibre of $(X_0,f_0)$ is homotopy equivalent to the bouquet of the Milnor fibres of the isolated singularities into which it splits.

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be holomorphic function-germs with isolated singularities at the origin, and let $f_*$ and $g_*$ be their initial forms. Suppose th…

Let $f,g\colon(\mathbb{C}^n,0)\to(\mathbb{C},0)$ be holomorphic function-germs, and write $f_*$ and $g_*$ for their initial forms. Suppose there is a homeomorphism…

Let $F$ be the Milnor fibre associated with a line arrangement, and let $\partial F$ be its boundary. Arrangement recoverability conjecture. The combinatorics of the arrangement ca…