Geometric Topology Papers of the Week

We bound the action of the mapping class group of (X,P) on the rational cohomology groups of the ordered configuration spaces F_n(X-P) of X-P. In particular, we show that, when #P < 2, the diagonal action of the mapping class group on the direct sum of the H^n(F_n(X-P)) is faithful, and determine its kernel when #P > 1.

In this paper, we establish several nonvanishing results for Floer lasagna modules $\mathcal{FL}(W,K)$ for a smooth compact connected oriented $4$-manifold $W$ and a knot $K\subset \partial W$, via the evaluation maps to link Floer homology.

We prove that the stabilizer of a reflection mirror of the Couwenberg-Heckman-Looijenga lattice $\mathcal{C}(G_{29},3)$ induces a nonarithmetic lattice in $\operatorname{PU}(2,1)$.

In this paper, we prove that the residual map is a locally trivial topological fibration over each open flat of the stratification induced by the resonance arrangement.

Beginning with Kuperberg's work on unknot recognition, several fundamental decision problems in 3-manifold topology have been shown to be in coNP assuming the generalized Riemann hypothesis. In this note, we explain how recent developments around the quasi-Riemann hypothesis yield unconditional versions of these results, leading for example to the first unconditional proof that 3-sphere recognition is in coNP.

We obtain new constraints on the topology of Lagrangian submanifolds in the standard symplectic vector space $\mathbb{C}^n$ using Floer theory on the based loop space, generalizing a theorem of Fukaya-Irie.

The ensemble average of Narain conformal field theories over their moduli space is a real-analytic Eisenstein series, whose Poincaré expansion can be interpreted as a sum over lens spaces weighted by the partition functions of Abelian Chern-Simons theory. In this paper we extend this correspondence from lens spaces to Seifert manifolds, which gives an example of a restricted sum over topologies of the kind that arises in three-dimensional quantum gravity.

We introduce a new surgical operation on Anosov flows, which we call bicontact padding surgery.

We study global Calabi flows $g(t)$ on compact Kähler surfaces with a uniform Sobolev constant.

Every link in the \(3\)-sphere admits a generalised \(T\)-link presentation. In this paper, we give an explicit polynomial-time algorithm which, given a signed Artin braid word and the number of strands, computes such a presentation.

We study the asymptotic distribution of the number of primitive, closed geodesics on Weil-Petersson random hyperbolic surfaces with genus $g$ and $n(g)$ cusps, under various growth rates of $n(g)$ as $g\to\infty$.

In this paper, we establish a topological classification of Bazaikin spaces whose sixth cohomology groups have orders prime to \(5\).

Following the knot-quiver correspondence, we investigate quiver counterparts of the HOMFLYPT skein relations by interpreting link invariants in terms of holomorphic worldsheets and their multicover contributions. Extending this framework to more general worldsheet geometries, we conjecture that, up to quiver equivalence, the adjacency matrix of the quiver associated with any link in a skein triple admits a block decomposition whose diagonal blocks are quiver adjacency matrices associated with the other two links.

We prove that any representation of $\pi_1(S)$ into $\mathrm{PSL}(2,\mathbb{R})$ with Euler class $3-2g$ is the holonomy of a hyperbolic metric on $S$ with one simple branch point.

We survey the recent development of spinal open books and nearly Lefschetz fibrations.

To investigate how our method scales, we use the technique of IsoFLOP curves on 15-tetrahedron triangulations of the 3-sphere, over a compute range of 6 to 3000 petaFLOPs, and observe neural scaling behaviour.

We advance Singhof's program of simplifying the sectors of a filling and their intersections.

We give invariants of pairs $(M,\Gamma)$ consisting of a closed connected oriented three-manifold and an oriented framed ribbon graph embedded in $M$ colored by a the Drinfeld center of a unimodular chromatic category $\mathcal C$.

We study codimension one homoclinic flows on closed surfaces and introduce a complete topological invariant based on the structural graph of the flow and the distinguishing graphs of its atoms.

We show that the L-polynomials are finite type invariants of order one.