math.GT daily digest: 4 new submissions for 26 June 2026

Issue note

On quasi-holomorphic homotopies of immersions of 3-manifolds into 5-manifolds

The notion of a quasi-holomorphic homotopy of two immersions of a $3$-manifold into a $5$-manifold extends the notion of their regular homotopy by also allowing the homotopy to pass through instances of maps with an isolated singularity around which the path of the homotopy forms a cross-cap (complex Whitney umbrella). We describe the local form of such homotopies and explain connections with the theory of holomorphic map germs from to . Our main result is a complete a description of how the fundamental group of the complement of the image of an immersion of a $3$-manifold into a $5$-manifold (i.e. its knot group) changes under a quasi-holomorphic homotopy. As a corollary we will see that certain quasi-holomorphic homotopies of the standard embedding of the $3$-sphere into the $5$-sphere do not change its knot group.

Integrality of genus-$g$ indices with adjoint Reidemeister torsions of twist knots

We consider the sum of the adjoint Reidemeister torsions and prove the integrality for twist knots and the meridian. We also give some concrete examples of the generating functions for these sums.

Distinguishing Gromov-Thurston manifolds using algebraic Dehn fillings

We develop criteria to distinguish the homotopy types of Gromov-Thurston manifolds. Our approach is based on a description of their fundamental groups as virtual Dehn fillings of relatively hyperbolic groups.

On L-space surgeries on two-bridge links

We classify the sets of $L$-space surgeries on all two-bridge links, providing the first examples of hyperbolic links for which such sets cannot be described as unions of finitely many rectangles in . The proof relies on several different techniques, each of which is applicable in greater generality: we introduce a sufficient diagrammatic condition for links in to be persistently foliar, a property that implies that every non-trivial surgery on such links supports a coorientable taut foliation. We define a simplified model for the Heegaard Floer homology of rational surgeries on two-component $L$-space links, following the work of Manolescu-Ozsváth, Liu, and Zemke, and use it to obtain obstructions to $L$-space surgeries. Finally, we use explicit computations of Turaev torsions to determine $L$-space surgeries in the case of generalised $L$-space links. Among the consequences of our results, we obtain an optimal uniform bound on the volume of any hyperbolic $L$-space that is surgery on a two-bridge link, together with a classification of all $L$-space satellite knots whose associated two-component pattern link is a two-bridge link.