Related papers: The Heisenberg 3-manifold is canonically oriented

Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally…

It is well known that every compact oriented 3-manifold admits an ideal triangulation, and that any two such triangulations with at least two ideal tetrahedra are related by a sequence of Pachner $2$-$3$ moves. Motivated by constructions in…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.

In this paper, we characterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in Minkowski 3-spaces.

We construct an invariant of closed oriented $3$-manifolds using a finite dimensional, involutory, unimodular and counimodular Hopf algebra $H$. We use the framework of normal o-graphs introduced by R. Benedetti and C. Petronio, in which…

We give a short proof of Waldhausen's homeomorphism theorem for orientable Haken 3-manifolds.

We characterize the closed, oriented, Seifert fibered 3-manifolds which are oriented boundaries of Stein manifolds. We also show that for this class of 3-manifolds the existence of Stein fillings is equivalent to the existence of symplectic…

In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean ${\Bbb{R}}^3$ and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces…

The Heisenberg curve is defined to be the curve corresponding to an extension of the projective line by the Heisenberg group modulo $n$, ramified above three points. This curve is related to the Fermat curve and its group of automorphisms…

We give an algebraic construction of orientation data for the Hilbert scheme of 0-dimensional subschemes of a smooth projective threefold endowed with a choice of square root of the canonical sheaf.

In short geometrization conjecture of W.\,Thurston (finally proved by G.~Perelman) says that any oriented $3$-manifold can be canonically partitioned into pieces, which have a geometric structure of one of the eight types. In the seminal…

We investigate the global topology of 3-dimensional Hessian manifolds. We prove that any compact, orientable 3-dimensional Hessian manifold is either a Hantzsche-Wendt manifold or admits the structure of a K\"ahler mapping torus. We analyze…

We survey, complete, and modify a proof, involving knot theory, of Stiefel's theorem that all orientable $3$-manifolds are parallelizable. The completion of the proof is done by using the relationship between the tangent bundle and normal…

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups…

We show that the number of isometry classes of cusped hyperbolic $3$-manifolds that bound geometrically grows at least super-exponentially with their volume, both in the arithmetic and non-arithmetic settings.

We prove that every closed oriented 3-manifold admits a hyperbolic cone-manifold structure with cone-angle arbitrarily close to 2pi.

A linearized version of Heisenberg's fundamental equation is quantized by path integral method.

We define a trisection of a closed, orientable three dimensional manifold into three handlebodies, and a notion of stabilization for these trisections. Several examples of trisections are described in detail. We define the trisection genus…