Related papers: Harmonic maps M^3 --> S^1 and 2-cycles, realizing …

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the ``piecewise geometric'' ones in the sense of…

Let $(\varphi_t)$, $(\phi_t)$ be two one-parameter semigroups of holomorphic self-maps of the unit disc $\mathbb D\subset \mathbb C$. Let $f:\mathbb D \to \mathbb D$ be a homeomorphism. We prove that, if $f \circ \phi_t=\varphi_t \circ f$…

Every element in the first cohomology group of a 3--manifold is dual to embedded surfaces. The Thurston norm measures the minimal `complexity' of such surfaces. For instance the Thurston norm of a knot complement determines the genus of the…

Let F be a fibration on a simply-connected base with symplectic fibre (M, \omega). Assume that the fibre is nilpotent and T^{2k}-separable for some integer k or a nilmanifold. Then our main theorem, Theorem 1.8, gives a necessary and…

We prove a sufficient condition for a \emph{pattern} $\pi$ on a \emph{triod} $T$ to have \emph{rotation number} $\rho_{\pi}$ coincide with an end-point of its \emph{forced rotation interval} $I_{\pi}$. Then, we demonstrate the existence of…

We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link $L$ in $S^3$. We then specialise this…

We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E_8\times E_8 symmetry. By considering particular…

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of…

We define an infinite sequence of new invariants, delta_n, of a group G that measure the size of the successive quotients of the derived series of G. In the case that G is the fundamental group of a 3-manifold, we obtain new 3-manifold…

The Thurston norm of a 3-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of 3-manifolds $M$ with $b_1(M) = 2$, and whose fundamental groups admit…

While there may be many Thurston metric geodesics between a pair of points in Teichm\"uller space, we find that by imposing an additional energy minimization constraint on the geodesics, thought of as limits of harmonic map rays, we select…

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

Classical work of Thurston and Gabai shows that finitely many taut sutured manifold hierarchies determine the Thurston norm of a compact oriented irreducible $3$-manifold with toroidal boundary. We give an explicit procedure to extract this…

We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We focus on the case when the fiber is a once-punctured torus (\Sigma_{1,1}). The corresponding 3d field theories can be realized using duality…

We show that the Alexander and Thurston norms are the same for all irreducible Eisenbud-Neumann graph links in homology 3-spheres. These are the links obtained by splicing Seifert links in homology 3-spheres together along tori. By…

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations…

A diffeomorphism between the twistor spaces of two Riemannian metrics on a smooth manifold preserving the fibres is defined based on a well-known construction. It is shown that this bundle isomorphim is a holomorphic map with respect to the…

Locally stable maps $S^3\to\mathbb{R}^4$ are classified up to homotopy through locally stable maps. The equivalence class of a map $f$ is determined by three invariants: the isotopy class $\sigma(f)$ of its framed singularity link, the…

We study Thurston's Lipschitz and curve metrics, as well as the arc metric on the Teichmueller space of one-hold tori equipped with complete hyperbolic metrics with boundary holonomy of fixed length. We construct natural Lipschitz maps…

Let $\Sigma$ and $\Sigma'$ be two refinements of a fan $\Sigma_0$ and $f \colon X_{\Sigma} \dashrightarrow X_{\Sigma'}$ be the birational map induced by $X_{\Sigma} \rightarrow X_{\Sigma_0} \leftarrow X_{\Sigma'}$. We show that the graph…