text: 245,60,1351360048988123136,32965031,Sami Douba,"New paper on arXiv 🙃 A corollary of the main result is that the fundamental group of the mapping torus of a Dehn twist on a closed oriented surface of positive genus does not embed in a compact Lie group. Comments welcome. <LINK> @littmath If the mapping class is pseudo-Anosov (and the surface has genus &gt; 1), the mapping torus is a closed hyperbolic 3-manifold. The fundamental group of such a manifold is virtually special (Agol) and hence embeds in a compact Lie group (also Agol): <LINK> @ryleealanza Thanks 💜 @littmath Yes; these groups are residually finite. However, the image of an element representing that curve under any representation into a compact Lie group will have finite order (and that's how I concluded that no such representation is faithful) @littmath Thanks for the interest! @AndyPutmanMath @MarissaKawehi Thank you! @agolian Button's sequence of papers in which he proves that fact and several similar ones were my starting point for this project. It's not immediately clear to me how the two facts are related, or whether there is a unified way to approach/prove them. @MachineInf @littmath I think it's pretty cool! @agolian What I show in the case of the mapping torus of a Dehn twist about a curve [c] is that the image of c under any finite-dimensional representation of pi_1(fibration) is quasi-unipotent. This won't be true for the monodromy (the cyclic subgroup generated by the latter is a retract) @agolian That detail is not contained in the abstract (it's buried somewhere in the introduction; maybe I should change that). Thanks!",https://arxiv.org/abs/2101.06797,"Let $M$ be a graph manifold containing a single JSJ torus $T$ and whose JSJ blocks are of the form $\Sigma \times S^1$, where $\Sigma$ is a compact orientable surface with boundary. We show that if $M$ does not admit a Riemannian metric of everywhere nonpositive sectional curvature, then there is an essential curve on $T$ such that any finite-dimensional linear representation of $\pi_1(M)$ maps an element representing that curve to a matrix all of whose eigenvalues are roots of $1$. In particular, this shows that $\pi_1(M)$ does not admit a faithful finite-dimensional unitary representation, and gives a new proof that $\pi_1(M)$ is not linear over any field of positive characteristic. ",Virtually unipotent curves in some non-NPC graph manifolds,10,"['New paper on arXiv 🙃 A corollary of the main result is that the fundamental group of the mapping torus of a Dehn twist on a closed oriented surface of positive genus does not embed in a compact Lie group. Comments welcome. <LINK>', '@littmath If the mapping class is pseudo-Anosov (and the surface has genus &gt; 1), the mapping torus is a closed hyperbolic 3-manifold. The fundamental group of such a manifold is virtually special (Agol) and hence embeds in a compact Lie group (also Agol): https://t.co/MtyOFpPoU0', '@ryleealanza Thanks 💜', ""@littmath Yes; these groups are residually finite. However, the image of an element representing that curve under any representation into a compact Lie group will have finite order (and that's how I concluded that no such representation is faithful)"", '@littmath Thanks for the interest!', '@AndyPutmanMath @MarissaKawehi Thank you!', ""@agolian Button's sequence of papers in which he proves that fact and several similar ones were my starting point for this project. It's not immediately clear to me how the two facts are related, or whether there is a unified way to approach/prove them."", ""@MachineInf @littmath I think it's pretty cool!"", ""@agolian What I show in the case of the mapping torus of a Dehn twist about a curve [c] is that the image of c under any finite-dimensional representation of pi_1(fibration) is quasi-unipotent. This won't be true for the monodromy (the cyclic subgroup generated by the latter is a retract)"", ""@agolian That detail is not contained in the abstract (it's buried somewhere in the introduction; maybe I should change that). Thanks!""]",21,01,1571