Related papers: Point-pushing in 3-manifolds

The geometrisation theorem of 3-manifolds was conjectured by Thurston the 1980s and proved by Perelman in the 2000s. This is an overview on the subject. We explain the content of the theorem and describe its effects in various situations.

We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In the thin parts of the manifold, we give effective bounds on the change in complex length of a…

We prove an a priori estimate of type sup*inf on Riemannian manifold of dimension 3 (not necessarily compact).

We analyze the three point Pick interpolation problem on the bidisk

In this paper, we study polyhedral 3-manifolds with nonnegative curvature and integral monodromy, two conditions motivated by Thurston's work in arXiv:math/9801088. We classify the 32 isometry types of codimension 3 singularities in such…

We prove a homological stability theorem for unlinked circles in $3$-manifolds and give an application to certain groups of diffeomorphisms of 3-manifolds.

In this short note, we study the injectivity radius bound for three dimensional complete and non-compact Riemannian manifold with good leaf foliations and with bounded curvature up to first order. We obtain the injectivity bound by using…

We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.

We present two proofs that all closed, orientable 3-manifolds are parallelisable. Both are based on the Lickorish-Wallace surgery presentation; one proof uses a refinement due to Kaplan and some basic contact geometry. This complements a…

We prove that for every compact, connected, differentiable 3--manifold $M$ there is a compact complex manifold $X$ which can be obtained from projective 3--space by a sequence of smooth, real blow ups and downs such that $M$ is…

In this article we establish the relation between the spines of 3-manifolds and the polyhedra with identified faces. We do this by showing that the spines of the closed, connected, orientable 3-manifolds can be presented through polyhedra…

In this paper, we study the obstruction for the sections of the universal hyperelliptic curves of genus $g\geq 3$. The obstruction of our interest comes from the relative completion of the hyperelliptic mapping class groups and the Lie…

Suppose a closed oriented $n$-manifold $M$ bounds an oriented $(n+1)$-manifold. It is known that $M$ $\pi_1$-injectively bounds an oriented $(n+1)$-manifold $W$. We prove that $\pi_1(W)$ can be residually finite if $\pi_1(M)$ is, and…

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

We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In…

In this paper, we give a new simplified calculation of the Lusternik-Schnirelmann category of closed 3-manifolds. We also describe when 3-manifolds have detecting elements and prove that 3-manifolds satisfy the equality of the Ganea…

We develop a method for constructing standard complexes which turns easy the calculation of their algebraic invariants and, as well, the precise evaluation of whether these complexes are embeddable or not in a 3-manifold. This method…

For a sequence of blow up solutions of the Yamabe equation on non-locally confonformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp…

This paper is a continuation of our previous paper, Co-Seifert fibrations of compact flat orbifolds, in which we developed the theory for classifying geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to…

In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…