34 problems

Casson invariant conjecture. The Casson invariant of $a3$ equals one-eighth the signature of the Milnor fiber.

Casson invariant conjecture. The Casson invariant of $\partial(X,o)$ is equal to one-eighth of the signature of the Milnor fiber of $(X,o)$.

Orlik–Randell's conjecture. The basis constructed by Orlik and Randell is distinguished, and its Seifert matrix is

Let $(X,0)$ be a cyclic quotient surface singularity of type $\frac{1}{n}(1,q)$ with $(n,q)=1$, let $L(n,q)$ be its link, and let $\mathcal{Z}_e\left(\frac{n}{n-q}\right)$ be Lisca…

Let $\Sigma$ be obtained by splicing homology spheres $\Sigma_1$ and $\Sigma_2$ along an edge of a splice diagram satisfying the semigroup condition. Let $F$, $F_1$, and $F_2$ be t…

Let $(X,o)$ be an isolated complete intersection surface singularity whose link $\Sigma$ is an integral homology $3$-sphere. The Casson Invariant Conjecture. The Casson invariant…

Orlik–Randell conjecture. For the fiber $X_1=\operatorname{Var}(Q-1)$, there is a finite-dimensional homogeneous vector space $U\subset R_n$ such that

Let $\mathcal{A}$ be an arrangement of lines in $\mathbb{CP}^2$, with Milnor fiber $F_\mathcal{A}$ and boundary three-manifold $\partial F_\mathcal{A}$. The combinatorics of…

Bobadilla's conjecture. Under these assumptions, $\Sigma f$ is smooth at $\mathbf 0$.

Torsion conjecture for Milnor fiber boundaries. (1) If

Let two hypersurface singularities be ambient-homeomorphic if their ambient spaces and singularities are related by an ambient homeomorphism, and let $F_f$ denote the Milnor fiber…

Let $F$ be the Milnor fiber of a central hyperplane arrangement, let $\lambda$ satisfy $\lambda^{|\mathcal{A}|}=1$, and let $H^k(F,\mathbb{C})_\lambda$ denote the $\lambda$-eigensp…

Let $f$ be a complex analytic function in $d$ variables vanishing at the origin $O$. Let $F_{f,O}$ be its topological Milnor fiber, let $\mathscr S_{f,O}$ be the motivic Milnor fib…

Milnor fiber conjecture. The Milnor fiber of $(X,o)$ is obtained by a four-dimensional splicing operation from the Milnor fibers associated to $\Gamma_a$ and $\Gamma_b$.

Splice-diagram decomposition conjecture. The Milnor fiber $F$ is homeomorphic to the result $\overline F$ of pasting

Cooper's conjecture. The subset $G$ is a deformation retract of $\overline{F_0}$. This conjecture gives a proposed combinatorial model for the Milnor fiber of a cycle type singular…

Let $f$ be a function in three variables, let $F_f$ be its Milnor fiber, and let $N$ be the nilpotent operator acting on $H^2(F_f,\mathbb C)$. Defective spectral-number eigenvector…

Let $M$ be a surface Milnor fiber of an $ADE$-type singularity, with its standard zero sections and standard Lagrangian spheres. ADE Lagrangian-sphere conjecture. Every Lagrangian…

Let ${\mathcal A}$ be a central essential plane arrangement in $\mathbb{C}^3$, defined by $f=\prod_{i=1}^r f_i$, and let … be its Milnor fiber. Let $H^i(F)_s$ be the eigenspace of…

Let $\mathcal{A}$ be a hyperplane arrangement over $\mathbb{C}$, with underlying matroid recording its combinatorial type, and let $F_{\mathcal{A}}$ denote its Milnor fiber. Orlik–…

Let ${\bf w}$ be an invertible polynomial, let $\Gamma_{\bf w}$ be its group of diagonal symmetries, and let $\check{V}_{\check{{\bf w}}}=\check{{\bf w}}^{-1}(1)$ be the Liouville…

Let $F_n^{(sk)\, c}$ and $F_n^{(sy)\, c}$ be the complements of the skew-symmetric and symmetric Milnor fibers, respectively. Let $S_{(\mathbf {m})}^{(sk)}$ and…

Let ${\mathcal A}$ be a real arrangement, let $F$ be its Milnor fiber, and let monodromy mean the action induced on the homology of $F$. A nontrivial monodromy has prime-power orde…

Let ${\mathcal A}$ be a real affine line arrangement and let $\overline{{\mathcal A}}$ be its projective arrangement. A sharp pair of lines is a pair of projective lines satisfying…

Let ${\mathcal A}$ be a real affine line arrangement, and let $\Gamma({\mathcal A})$ be the graph whose vertices are the lines $H\in{\mathcal A}$, with an edge $(H,H')$ exactly whe…