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Hongbin Sun

Publications and source records attributed to Hongbin Sun.

135 records · Page 8Linked to original sources
arXiv2014

Virtual Homological Torsion of Closed Hyperbolic 3-manifolds

In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $π_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. Using Agol and Wise's result that fundamental groups of hyperbolic 3-manifolds are LERF and quasi-convex subgroups are virtual retract, we will show that closed hyperbolic 3-manifolds virtually contain any prescribed homological torsion: For any finite abelian group $A$, and any closed hyperbolic 3-manifold $M$, there exists a finite cover $N$ of $M$, such that $A$ is a direct summand of $Tor(H_1(N;\mathbb{Z}))$.

math.GT↗
arXiv2014

Virtual Domination of $3$-manifolds

For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented $3$-manifold $N$, we will show that $M$ admits a finite cover $M'$, such that there exists a degree-$2$ map $f:M'\rightarrow N$, i.e. $M$ virtually $2$-dominates $N$.

math.GT↗
arXiv2013

A Transcendental Invariant of Pseudo-Anosov Maps

For each pseudo-Anosov map $ϕ$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,ϕ)$. $A(S,ϕ)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will develop a few nice properties of $A(S,ϕ)$ and give a few examples to show that $A(S,ϕ)$ is a nontrivial invariant. These nontrivial examples give an answer to a question asked by McMullen: the minimal point of the restriction of the dilatation function on fibered face need not be a rational point.

math.GT↗
arXiv2013

On slope genera of knotted tori in 4-space

In this note, we investigate genera for the slopes of a knotted torus in the 4-sphere analogous to the genus of a classical knot. We compare various formulations of this notion, and use this notion to study the extendable subgroup of the mapping class group of the knotted torus.

math.GT↗
arXiv2010

Finiteness of mapping degree sets for 3-manifolds

By constructing certain maps, this note completes the answer of the Question: For which closed orientable 3-manifold $N$, the set of mapping degrees $cD(M,N)$ is finite for any closed orientable 3-manifold $M$?

math.GT↗
arXiv2010

On fibered commensurability

This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability class contains a unique minimal element, whereas the class of Seifert manifolds fibering over the circle consists of a single commensurability class with infinitely many minimal elements. The situation for non-geometric manifolds is more complicated, and we illustrate a range of phenomena that can occur in this context.

math.GT↗
arXiv2008

Self-mapping degrees of torus bundles and torus semi-bundles

Each closed oriented 3-manifold $M$ is naturally associated with a set of integers $D(M)$, the degrees of all self-maps on $M$. $D(M)$ is determined for each torus bundle and torus semi-bundle $M$. The structure of torus semi-bundle is studied in detail. The paper is a part of a project to determine $D(M)$ for all 3-manifolds in Thurston's picture.

math.GT↗