Related papers: Closed surface bundles of least volume

This paper gives a uniform, self-contained and direct approach to a variety of obstruction-theoretic problems on manifolds of dimension 7 and 6. We give necessary and sufficient cohomological criteria for the existence of various…

We show that the number of square-tiled surfaces of genus $g$, with $n$ marked points, with one or both of its horizontal and vertical foliations belonging to fixed mapping class group orbits, and having at most $L$ squares, is asymptotic…

We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $\chi$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This…

Let $S$ be a compact hyperbolic Riemann surface of genus $g \geq 2$. We call a systole a shortest simple closed geodesic in $S$ and denote by $\mathop{sys}(S)$ its length. Let $\mathop{msys(g)}$ be the maximal value that…

We obtain new lower bounds of the minimal genus of a locally flat surface representing a 2-dimensional homology class in a topological 4-manifold with boundary, using the von Neumann-Cheeger-Gromov $\rho$-invariant. As an application our…

Let $M$ be a 1-cusped hyperbolic 3-manifold. In this paper, we study the behavior of $N_M(v)$, the number of Dehn fillings of $M$ with a given volume $v(\in \mathbb{R})$. We conduct extensive computational experiments to estimate $N_M$ and…

We consider orientation-preserving actions of finite groups $G$ on pairs $(S^3, \Sigma)$, where $\Sigma$ denotes a compact connected surface embedded in $S^3$. In a previous paper, we considered the case of closed, necessarily orientable…

Let $S$ be a ruled surface inside a smooth threefold $W$ and let $E$ be a vector bundle on a formal neighborhood of $S.$ We find minimal conditions under which the local moduli space of $E$ is finite dimensional and smooth. Moreover, we…

For a twist knot $\mathcal{K}_{p'}$, let $M$ be the closed $3$-manifold obtained by doing $(p, q)$ Dehn-filling along $\mathcal{K}_{p'}$. In this article, we prove that Chen-Yang's volume conjecture holds for sufficiently large $|p| + |q|$…

We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.

Let W be a compact manifold and let \rho be a representation of its fundamental group into PSL(2,C). The volume of \rho is defined by taking any \rho-equivariant map from the universal cover of W to H^3 and then by integrating the pull-back…

Suppose an orientation preserving action of a finite group $G$ on the closed surface $\Sigma_g$ of genus $g>1$ extends over the 3-torus $T^3$ for some embedding $\Sigma_g\subset T^3$. Then $|G|\le 12(g-1)$, and this upper bound $12(g-1)$…

We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a new seminorm on exact bounded cohomology, we use these…

Let $(M^{n+1},g)$ be a closed Riemannian manifold of dimension $3\le n+1\le 5$. We show that, if the metric $g$ is generic or if the metric $g$ has positive Ricci curvature, then $M$ contains infinitely many geometrically distinct constant…

We show how certain stabilizations produce infinitely many closed oriented 4-manifolds which are the total spaces of genus g surface bundles (resp. Lefschetz fibrations) over genus h surfaces and have non-zero signature, but do not admit…

We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many…

We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed…

In this paper, we demonstrate that any asymptotically flat manifold $(M^n, g)$ with $4\leq n\leq 7$ can be foliated by a family of area-minimizing hypersurfaces, each of which is asymptotic to Cartesian coordinate hyperplanes defined at an…

We extend the concept of renormalized volume for geometrically finite hyperbolic $3$-manifolds, and show that is continuous for geometrically convergent sequences of hyperbolic structures over an acylindrical 3-manifold $M$ with…

In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…