11 problems

A Thom–Boardman class is a singularity class indexed by a sequence of nonnegative integers, and its Thom polynomial is the universal cohomology class representing the locus of maps…

Assume $l\geq 1$. Let $\underline{\eta}$ be a Mather T- or S-multisingularity, let $M(l)$ be the Mather bound, and let $\mathcal{C}_l$ be the class of maps under consideration. Wri…

Assume $l\geq 1$. Let $\mathcal{C}_l$ be the class of maps under consideration, let $\underline{\eta}$ be a T- or S-multisingularity, and let…

Let $T^{\mathrm{SSM}}(\tau,\ell)$ denote an SSM-Thom polynomial of a singularity $\tau$ and relative dimension $\ell$. For $\ell=0$, the SSM-Thom polynomials have alternating signs…

Cobordism conjecture. This cobordism is oriented if $M$ and $N$ are oriented, the codimension $k$ is odd, and $r$ is even.

Bérczi's neighbouring-coefficient conjecture. The quotient

Rimányi's positivity conjecture. The coefficients of the Thom polynomial are nonnegative, equivalently

Thom-polynomial coefficient-ratio conjecture. One has

Rimányi's conjecture. For every such multiindex, the coefficient is nonnegative:

Localization-form conjecture. If part (a) of the generating-function conjecture holds, then

Let $Q$ be a $[?]$-dimensional, commutative, nilpotent algebra with $\deg(\operatorname{tp}_Q(l))=\mu\cdot l+\gamma$. Write … and let $\operatorname{RES}$ denote the iterated resid…