40 citations · 111 across the 22 of their papers we have counts for
22 papers · 1 filter
Barbell twists are natural
Yi Liu
For any oriented smooth --manifold diffeomorphic to (), the author establishes a natural isomorphism of abelian groups: $$\mathrm{Mod}…
On Hempel pairs and Turaev--Viro invariants
Yi Liu
Surface bundles arising from periodic mapping classes may sometimes have non-isomorphic, but profinitely isomorphic fundamental groups. Pairs of this kind have been discovered by H…
Virtual homological eigenvalues and the Weil--Petersson translation length
Yi Liu
For any pseudo-Anosov automorphism on an orientable closed surface, an inquality is established bounding certain growth of virtual homological eigenvalues with the Weil--Petersson…
Finite quotients, arithmetic invariants, and hyperbolic volume
Yi Liu
For any pair of orientable closed hyperbolic --manifolds, this paper shows that any isomorphism between the profinite completions of their fundamental groups witnesses a bijecti…
Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
Yi Liu
For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of t…
Volume of Seifert representations for graph manifolds and their finite covers
Pierre Derbez, Yi Liu, Shicheng Wang
For any closed orientable 3-manifold, there is a volume function defined on the space of all Seifert representations of the fundamental group. The maximum absolute value of this fu…
Mapping classes are almost determined by their finite quotient actions
Yi Liu
Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on the profi…
Virtual homological spectral radii for automorphisms of surfaces
Yi Liu
In this paper, it is shown that any surface automorphism of positive mapping-class entropy possesses a virtual homological eigenvalue which lies outside the unit circle of the comp…
Volume of representations and mapping degree
Pierre Derbez, Yi Liu, Hongbin Sun +1
Given a connected real Lie group and a contractible homogeneous proper --space furnished with a --invariant volume form, a real valued volume can be assigned to any repre…
Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic 3-manifolds
Yi Liu
In this paper, it is shown that every closed hyperbolic 3-manifold contains an immersed quasi-Fuchsian closed subsurface of odd Euler characteristic. The construction adopts the go…
Positive simplicial volume implies virtually positive Seifert volume for -manifolds
Pierre Derbez, Yi Liu, Hongbin Sun +1
In this paper, it is shown that for any closed orientable -manifold with positive simplicial volume, the growth of the Seifert volume of its finite covers is faster than the lin…
Degree of -Alexander torsion for 3-manifolds
Yi Liu
For an irreducible orientable compact -manifold with empty or incompressible toral boundary, the full --Alexander torsion associated to any real first…
A characterization of virtually embedded subsurfaces in 3-manifolds
Yi Liu
The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes a…
Chern--Simons theory, surface separability, and volumes of 3-manifolds
Pierre Derbez, Yi Liu, Shicheng Wang
We study the set of volumes of all representations $ρ\coπ_1M\to G$, where is a closed oriented -manifold and is either ${\rm Iso}_+{\Hi}^3$ o…
Homology of curves and surfaces in closed hyperbolic 3-manifolds
Yi Liu, Vladimir Markovic
Among other things, we prove the following two topologcal statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manif…
Virtual cubulation of nonpositively curved graph manifolds
Yi Liu
In this paper, we show that a nontrivial compact graph manifold is nonpositively curved if and only if its fundamental group virtually embeds into a right-angled Artin group. As a…
On slope genera of knotted tori in 4-space
Yi Liu, Yi Ni, Hongbin Sun +1
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, an…
A Jorgensen-Thurston theorem for homomorphisms
Yi Liu
In this note, we provide a description of the structure of homomorphisms from a finitely generated group to any torsion-free (3-dimensional) Kleinian group with uniformly bounded f…
Finiteness of nonzero degree maps between three-manifolds
Yi Liu
In this paper, it is shown that every orientable closed 3-manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible non-geometric orientabl…
Presentation length and Simon's conjecture
Ian Agol, Yi Liu
In this paper, we show that any knot group maps onto at most finitely many knot groups. This gives an affirmative answer to a conjecture of J. Simon. We also bound the diameter of…
Spin structures and codimension-two homeomorphism extensions
Fan Ding, Yi Liu, Shicheng Wang +1
Let $\imath: M\to \RR^{p+2}$ be a smooth embedding from a connected, oriented, closed -dimesional smooth manifold to $\RR^{p+2}$, then there is a spin structure $\imath^\sharp(ς…
Extending automorphisms over $\RR^{p+2}$ and realizing DE attractors
Fan Ding, Yi Liu, Shicheng Wang +1
In this paper we consider the realization of DE attractors by self-diffeomorphisms of manifolds. For any expanding self-map of a connected, closed -dimensional manifo…