8 problems

A left orderable group is a group admitting a total order invariant under left multiplication, and a group is locally indicable if every nontrivial finitely generated subgroup has…

Lifschitz–Witte Morris conjecture. If

Let $M$ be an orientable graph manifold with infinite fundamental group. A circularly orderable manifold is one whose fundamental group admits a circular order; write $CO$ when thi…

Let $M$ be an orientable, compact, connected, irreducible $3$-manifold. Write $LO$ when the fundamental group of $M$ is left-orderable, $NLS$ when $M$ is not an $L$-space, and…

Let $B_n$ be the braid group on $n$ strands, let $\mathbb{E}$ be the relevant ordered field with quadratic form $Q$, and let … be the reduced Burau representation. A braid…

A group is an $R^*$-group if it has no generalized torsion, and it is bi-orderable if it admits a strict total ordering invariant under both left and right multiplication. For a…

Dunfield's conjecture. For every rational slope $r\in I$, Dehn filling $K$ along slope $r$ is orderable.

Let $M$ be a rational homology $3$-sphere, meaning that $H_1(M;\mathbf{Q})=0$. Its Heegaard Floer homology has rank at least $\left|H_1(M;\mathbf{Z})\right|$, and $M$ is an L-space…