Related papers: Regularization of Gamma_1-structures in dimension …

We study deformations of geometric structures on some LVM manifolds of complex dimension $3$. More precisely, we study resonant structures, a particular type of $(G,X)$-structures, via the Ehresmann-Thurston principle, and their link with…

We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local…

If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that pi_1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In particular, we show this for tight…

We show that a complete non-compact 3-manifold with scalar curvature bounded below by a positive constant admits a singular foliation by surfaces of controlled area and diameter.

We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this…

We show that the correction terms in Heegaard Floer homology give a lower bound to the the genus of one-sided Heegaard splittings and the $\mathbb Z_2$--Thurston norm. Using a result of Jaco--Rubinstein--Tillmann, this gives a lower bound…

We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and…

W. Thurston proved that to a triangulation of the sphere of non-negative combinatorial curvature, one can associate an element in a certain lattice over the Eisenstein integers such that its orbit is a complete invariant of the…

We give a simpler and more conceptual proof that a morphism from a 3-fold to a surface, over an algebraically closed field of characteristic 0, can be made into a toroidal morphism by sequences of blow ups of nonsingular subvarieties above…

Thurston obtained a combinatorial characterization for generic branched self-coverings that preserve the orientation of the oriented 2-sphere by associating a planar graph to them [arXiv:1502.04760]. In this work, the Thurston result is…

We study codimension one foliations in projective space \PP^n over \CC by looking at its first order perturbations: unfoldings and deformations. We give special attention to foliations of rational and logarithmic type. For a differential…

This paper is a continuation of I, (same title), and is concerned with the existence, regularity and degeneration of metrics minimizing natural curvature functionals on the space of metrics on 3-manifolds. The functionals chosen are…

A Riemannian manifold is a called a good rational expander in dimension $i$ if every $i$-cycle bounds a rational $i+1$-chain of comparatively small volume. We construct 3-manifolds which are good expanders in all dimensions. On the other…

We study a bordism relation for stable 3-forms on a 6-manifold, which is a binary relation on the set of closed $SL(3;\mathbb{C})$-structures on a 6-manifold via closed $G_2$-structures. Under $SO(3)$-symmetry and a co-associative condition…

We show that a veering triangulation $\tau$ specifies a face $\sigma$ of the Thurston norm ball of a closed three-manifold, and computes the Thurston norm in the cone over $\sigma$. Further, we show that $\tau$ collates exactly the taut…

Given an orientable ideally triangulated $3$--manifold $M$, we define a system of real valued equations and inequalities whose solutions can be used to construct projective structures on $M$. These equations represent a unifying framework…

Thurston related $\mathbb{C}{\rm P}^1$-structures (complex projective structures) and equivariant pleated surfaces in the hyperbolic-three space $\mathbb{H}^3$, in order to give a parameterization of the deformation space of $\mathbb{C}{\rm…

In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds…

We recreate an unpublished proof of William Thurston from the early 1970's that any smooth 2-plane field on a manifold of dimension at least 4 is homotopic to the tangent plane field of a foliation.

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…