Related papers: Self-mapping Degrees of 3-Manifolds

We collect examples of genus two Heegaard diagrams for compact 3-manifolds admitting each of the eight Thurston geometries.

An automorphism on a complex supermanifold $\mathcal M$ is called unipotent if it reduces to the identity on the associated graded supermanifold $gr(\mathcal M)$. These automorphisms are close to be complementary to those responsible for…

For $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting…

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…

For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless…

In [3] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for proper maps between orbifolds, which counts preimages of…

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 prove that for any oriented cusped hyperbolic 3-manifold $M$ and any compact oriented 3-manifold $N$ with tori boundary, there exists a finite cover $M'$ of $M$ that admits a degree-8 map $f:M'\to N$, i.e. $M$ virtually 8-dominates $N$.

We investigate the behavior of the higher-order degrees, db_n, of a finitely presented group G. These db_n are functions from H^1(G;Z) to Z whose values are the degrees certain higher-order Alexander polynomials. We show that if def(G) is…

For any closed oriented 3-manifold $M$ with positive simplicial volume and any closed oriented 3-manifold $N$, we prove that there exists a finite cover $M'$ of $M$ that admits a degree-1 map $f:M'\to M$, i.e. M virtually 1-dominates N.…

The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…

We establish a new homological lower bound for the Thurston norm on 1-cohomology of 3-manifolds. This generalizes previous results of C. McMullen, S. Harvey, and the author. We also establish an analogous lower bound for 1-cohomology of…

This is a problem list in the theory of foliations and laminations of 3-manifolds. The focus is on the relationship of foliations and laminations with other aspects of 3-manifold topology, especially with the Thurston theory of geometric…

We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlying number field. This does not solve the open question…

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, including constructive proofs, but there has been little attention to the…

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

A method is developed here for building differentiable three-dimensional manifolds on multicube structures. This method constructs a sequence of reference metrics that determine differentiable structures on the cubic regions that serve as…

We show that a closed orientable 3--dimensional manifold admits a round fold map into the plane, i.e. a fold map whose critical value set consists of disjoint simple closed curves isotopic to concentric circles, if and only if it is a graph…

In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted…