192 citations · 749 across the 37 of their papers we have counts for
38 papers · 1 filter
Ribbon concordance of fibered knots and compressions of surface homeomorphisms
Ian Agol, Qiuyu Ren
We prove that simplicial volume and dilatation are monotone under ribbon concordance between fibered knots in , and that every fibered knot has only finitely many predecessors…
Simply transitive geodesics and omnipotence of lattices in PSL
Ian Agol, Tam Cheetham-West, Yair Minsky
We show that the isometry group of a finite-volume hyperbolic 3-manifold acts simply transitively on many of its closed geodesics. Combining this observation with the Virtual Speci…
Chainmail links and L-spaces
Ian Agol
In this note we prove that alternating chainmail links are L-space links. The proof is inspired by corresponding proofs for double branched covers of alternating links. We also mor…
Guts in Sutured Decompositions and the Thurston Norm
Ian Agol, Yue Zhang
We construct an invariant called guts for second homology classes in irreducible 3-manifolds with toral boundary and non-degenerate Thurston norm. We prove that the guts of second…
Peripheral birationality for 3-dimensional convex co-compact varieties
Ian Agol, Franco Vargas Pallete
Let be a hyperbolizable -manifold with boundary, and let be a component of the -character variety of that contains the convex co-compact charac…
Ribbon concordance of knots is a partial order
Ian Agol
In this note we show that ribbon concordance forms a partial ordering on the set of knots, answering a question of Gordon. The proof makes use of representation varieties of the kn…
Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications
Ian Agol, Chi Cheuk Tsang
We study the strongly connected components of the flow graph associated to a veering triangulation, and show that the infinitesimal components must be of a certain form, which have…
Congruence RFRS towers
Ian Agol, Matthew Stover
We describe a criterion for a real or complex hyperbolic lattice to admit a RFRS tower that consists entirely of congruence subgroups. We use this to show that certain Bianchi grou…
Rigidity in hyperbolic Dehn filling
Ian Agol, BoGwang Jeon
This paper concerns with a rigidity of core geodesics in hyperbolic Dehn fillings. For instance, for an -cusped hyperbolic -manifold having non-symmetric cusp shapes, we…
Embedding Heegaard Decompositions
Ian Agol, Michael H. Freedman
A smooth embedding of a closed -manifold in may generically be composed with projection to the fourth coordinate to determine a Morse function on and henc…
Hyperbolic four-manifolds with vanishing Seiberg-Witten invariants
Ian Agol, Francesco Lin
We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in ge…
Certifying the Thurston norm via SL(2, C)-twisted homology
Ian Agol, Nathan M. Dunfield
We study when the Thurston norm is detected by twisted Alexander polynomials associated to representations of the 3-manifold group to SL(2, C). Specifically, we show that the hyper…
Pseudo-Anosov stretch factors and homology of mapping tori
Ian Agol, Christopher J. Leininger, Dan Margalit
We consider the pseudo-Anosov elements of the mapping class group of a surface of genus g that fix a rank k subgroup of the first homology of the surface. We show that the smallest…
Simplifying 3-manifolds in R^4
Ian Agol, Michael H. Freedman
We show that a smooth embedding of a closed 3-manifold in S^3 x R can be isotoped so that every generic level divides S^3 x t into two handlebodies (i.e., is Heegaard) provided the…
Min-max theory and the energy of links
Ian Agol, Fernando C. Marques, André Neves
Freedman, He, and Wang, conjectured in 1994 that the Mobius energy should be minimized, among the class of all nontrivial links in Euclidean space, by the stereographic projection…
The virtual Haken conjecture
Ian Agol, Daniel Groves, Jason Manning
We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subg…
Ideal Triangulations of Pseudo-Anosov Mapping Tori
Ian Agol
We show how to construct an ideal triangulation of a mapping torus of a pseudo-Anosov map punctured along the singular fibers. This gives rise to a new conjugacy invariant of mappi…
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…
The minimal volume orientable hyperbolic 2-cusped 3-manifolds
Ian Agol
We prove that the Whitehead link complement and the (-2, 3, 8) pretzel link complement are the minimal volume orientable hyperbolic 3-manifolds with two cusps, with volume 3.66...…
Bounds on exceptional Dehn filling II
Ian Agol
We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determinin…
Pants immersed in hyperbolic 3-manifolds
Ian Agol
We show that an immersed thrice-punctured sphere in a cusped orientable hyperbolic 3-manifold is either embedded or has a single clasp in a manifold obtained by hyperbolic Dehn fil…
Criteria for virtual fibering
Ian Agol
We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimens…
Singular surfaces, mod 2 homology, and hyperbolic volume, II
Marc Culler, Peter B. Shalen
If M is a closed simple 3-manifold whose fundamental group contains a genus-g surface group for some g>1, and if the dimension of H_1(M;Z_2) is at least max(3g-1,6), we show that M…
Systoles of hyperbolic 4-manifolds
Ian Agol
We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.