29 problems

A compact lamination $(L,\mathcal L)$ embedded in a manifold $M$ is preserved by a diffeomorphism $f$ and is normally $AS$ if there exists $\epsilon>0$ such that the saturated nonw…

Let $S$ be a surface, let $\mathcal{T}(S)$ be its Teichmüller space, and fix a measured lamination $\lambda$ on $S$. Grafting along $\lambda$ induces a self-map of $\mathcal{T}(S)$…

Symmetry conjecture. Non-injectivity only happens when $f$ or a power of $f$ has a Möbius symmetry.

Ending laminations are laminations associated with the ends of geometrically infinite surface groups, while pleating laminations describe the bending data of pleated surfaces bound…

Let $\rho$ be an $\mathrm{SL}(2,\mathbb C)$ character and let ${{\mathcal E}(\rho)}$ denote its set of end invariants, viewed as a subset of the projective lamination space…

Tameness Conjecture. The automorphism $f$ can be isotoped so that it preserves the splitting and the induced automorphism $g$ on $H_1$ is train-track generic and has a tame one-dim…

Let $\mathcal L$ be a lamination arising from a group action. A fidelity of $\mathcal L$ is a germ map into a path-connected space whose induced map on fundamental germ groupoids i…

Unique ergodicity conjecture. For any Laplace operator on the base of a suspension, the conclusion of unique ergodicity on a minimal suspension holds.

Let $H$ be a handlebody with invariant measured lamination $\boldsymbol{\Lambda}$, and let the growth rate refer to the associated irreducible automorphism. A lamination is tight w…

Let $M$ be a compact, orientable, irreducible $3$-manifold and let $\lambda$ be a lamination in $M$. Assume that $\lambda$ has no sphere leaves and that, for every leaf $L$ of…

Let $\M_2$ be the Mandelbrot set, and let the space of quadratic topological polynomials be the monotone model of its boundary constructed from equivalence classes of diameters and…

A laminar group is a group admitting the relevant laminar action, and a very full lamination is a lamination all of whose gaps are finite-sided ideal polygons. Calegari's conjectur…

Tropical parametrization conjecture. The basis $\mathbb{I}_{\mathcal{X}}^q(\mathcal{L}_{\mathfrak{sl}_3}^p(Sigma,\mathbb{Z}))$ is parametrized by tropical points. Namely, for every…

Let $mathbb T_q$ be the tautological tree, whose ends determine sequences of $ell$-values and associated $F$-sequences. An end is big when … and it is of type $S$ when its associat…

Let $mathcal S_q$ be the shift locus in a one-dimensional slice, and let $mathbb T_q$ be the tautological tree whose ends correspond to components of the complement of…

Let $\mathscr{A}_{{\rm SL}_3,\frak{S}}(\mathbb{Z}^{T})$ be the set of tropical-integer points of the ${\rm SL}_3$ cluster $\mathscr{A}$-space of a generalized marked surface…

Let $\alpha=2$ and let $\nu$ be a critical equivalent of a weight sequence of $\alpha$-stable type, with $\nu$ having infinite variance. Let $(\tilde{B}_n)_{n\geq 0}$ be the sequen…

Let $(G,\operatorname{\mathcal{L}}_1,\operatorname{\mathcal{L}}_2)$ be a pseudo-fibered triple. Suppose that $G$ is finitely generated, torsion-free, and freely indecomposable. Pse…

Let $(\operatorname{\mathcal{L}},G)$ be a tight pair, where $G$ acts on the circle preserving the lamination system $\operatorname{\mathcal{L}}$. Tight-pair global fixed-point conj…

Let $\operatorname{QML}$ denote the quadratic minor lamination, and let the equivalence relation it induces on the circle identify points according to the leaves and classes of…

Let ${\boldsymbol{\mathcal F}}$ be the lamination considered in the paper, and let the main molecule denote the corresponding subset of the Mandelbrot set. DLS conjecture. The lami…

Fundamental Singularity Conjecture. Under these hypotheses, $\overline{\cal L}$ has the structure of a minimal lamination of $\mathbb{R}^3$.

Let $L\hookrightarrow M$ be a lamination with a transverse $\mathbb O$-measure or $\mathbb S$-measure $\nu$, carried by a codimension-$1$ branched manifold. A splitting of the bran…

Thurston's homeomorphism conjecture. The Mandelbrot set is homeomorphic to this model:

Let $G$ be a finitely generated torsion-free discrete subgroup of $\operatorname{Homeo_+}(S^1)$. A pants-like $\operatorname{COL}_2$ group has a pants-like collection of two invari…