Related papers: Framings and Projective Framings for 3-Manifolds

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change…

Applying Morse theory, we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional handlebodies. We also give a necessary and sufficient condition to determine the…

We classify projective manifolds with flat holomorphic conformal structures.

We show that if $F$ is a smooth, closed, orientable surface embedded in a closed, orientable 3-manifold $M$ such that for each Riemannian metric $g$ on $M$, $F$ is isotopic to a least-area surface $F(g)$, then $F$ is incompressible.

We show that a strongly irreducible and boundary-strongly irreducible surface can be isotoped to be almost normal in a triangulated 3-manifold.

We prove that any isometry between two dimensional Hilbert geometries is a projective transformation unless the domains are interiors of triangles.

Differentiable rendering is a technique to connect 3D scenes with corresponding 2D images. Since it is differentiable, processes during image formation can be learned. Previous approaches to differentiable rendering focus on mesh-based…

We show that if $M$ is an orientable 4-dimensional infrasolvmanifold and either $\beta=\beta_1(M;\mathbb{Q})\geq2$ or $M$ is a $\mathbb{S}ol_0^4$- or a $\mathbb{S}ol_{m,n}^4$-manifold (with $m\not=n$) then $M$ is parallelizable. There are…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…

When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers…

We give a sufficient condition for a first order infinitesimal deformation of a curve on a 3-fold to be obstructed. As application we construct generically non-reduced components of the Hilbert schemes of uniruled 3-folds and the Hom scheme…

Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is…

A real projective orbifold has a radial end if a neighborhood of the end is foliated by projective geodesics that develop into geodesics ending at a common point. It has a totally geodesic end if the end can be completed to have the totally…

We determine which 3-manifolds admit a unitary representation such that the corresponding twisted chain complex is acyclic.

Every homomorphism of modules is projective-stably equivalent to an epimorphism but is not always to a monomorphism. We prove that a map is projective-stably equivalent to a monomorphism if and only if its kernel is torsionless, that is, a…

We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…

We prove that if a prime 3-manifold M is not finitely covered by the 3-sphere or a product manifold, then M is virtually chiral, i.e. it has a finite cover that does not admit an orientation reversing self-homeomorphism. In general if a…