Minimal volume entropy vanishes or is positive under certain fiber growth conditions.
problem Conditions for minimal volume entropy to be zero or positive.
method Analyzes topological conditions related to fiber growth of maps.
result Examples of finite simplicial complexes with zero simplicial volume and large minimal volume entropy.
The paper studies entropy in branched covers of 3-manifolds.
problem Entropy of pseudo-Anosov monodromies in fibered 3-manifolds.
method Analyzes the minimal entropy of genus g surface bundles over the circle as 2-fold branched covers of 3-manifolds.
result There exist infinitely many 3-manifolds with comparable minimal entropy to 1/g.
Study positive entropy actions by higher-rank lattices, proving rigidity and conjugacy results.
problem Positive entropy actions by higher-rank lattices in Lie groups.
method Analysis of sub-actions, fiber entropy upper semicontinuity, and conjugacy arguments.
result Actions by higher-rank lattices in SL(n,R) are conjugate to affine actions on (infra-)tori. Improved bounds linking entropy and volume in hyperbolic 3-manifolds.
problem Establishing bounds between entropy and volume in hyperbolic 3-manifolds.
method Heegaard Floer homology and hyperbolic geometry.
result Entropy is bounded by hyperbolic volume with logarithmic factor.
We consider a hyperbolic surface bundle over the circle with the smallest known volume among hyperbolic manifolds having 3 cusps, so called "the magic manifold". We compute the entropy function on the fiber face of the unit ball with respect to the Thurston norm, determine homology classes whose representatives are gen…
Let b be a pseudo-Anosov braid whose permutation has a fixed point and let Mb be the mapping torus by the pseudo-Anosov homeomorphism defined on the genus 0 fiber Fb associated with b. This paper describes a structure of the fibered cone C of F for Mb. We prove that there is a 2-dimension…
Maps on infinite-type surfaces linked to 3-manifold flows.
problem Understanding maps on infinite-type surfaces using 3-manifold flows.
method Using pseudo-Anosov flows to construct maps from fibered hyperbolic 3-manifolds.
result Maps on infinite-type surfaces can be derived from fibered structures in 3-manifolds.
Study minimal volume entropy for free-by-cyclic groups and 2D right-angled Artin groups.
problem Characterize minimal volume entropy for aspherical simplicial complexes with these groups as fundamental groups.
method Algebraic and geometric characterization, using fiber π1-growth collapse and non-collapsing assumptions. result Provide bounds and criteria for minimal volume entropy in aspherical simplicial complexes.
A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every C1+α diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nod…
The study shows how energy density of harmonic maps dominates in n-Fuchsian fibers, leading to unique minimal surfaces.
problem Understanding energy density and topological invariants in n-Fuchsian fibers of Higgs bundles. method Establishing an algebraic inequality generalizing a GIT theorem to prove energy density domination.
result Energy density of harmonic maps dominates in n-Fuchsian fibers, leading to unique minimal surfaces. The study examines conditions for minimal volume entropy of simplicial complexes.
problem Conditions for minimal volume entropy of simplicial complexes.
method Topological conditions and growth of fundamental groups.
result Examples of simplicial complexes with zero simplicial volume and large minimal volume entropy.
Let M be a hyperbolic fibered 3-manifold. We study properties of sequences (Sαn,ψαn) of fibers and monodromies for primitive integral classes in the fibered cone of M. The main tool is the asymptotic translation length ℓC(ψαn) of the pseudo-Anosov monodromy ψαn on the curve …
Study integral simplicial volume of cyclic covers of torus bundles.
problem Asymptotic behavior of integral simplicial volume of cyclic covers.
method Integral filling volume invariant for monodromy, bounds established.
result Established both lower and upper bounds for the limit of integral simplicial volume.
Let δg be the minimal dilatation for pseudo-Anosovs on a closed surface Σg of genus g and let δg+ be the minimal dilatation for pseudo-Anosovs on Σg with orientable invariant foliations. This paper concerns the pseudo-Anosovs which occur as the monodromies on closed fibers for Dehn fillings of N(r) for…
The paper proves inequalities linking geometric norms and Thurston norms in hyperbolic 3-manifolds.
problem Inequalities linking geometric norms and Thurston norms in hyperbolic 3-manifolds.
method Analyzes geometric L2-norms, Thurston norms, and Lipschitz maps to prove inequalities. result Proves an inequality between geometric L2-norm and Thurston norm, qualitatively sharp. New polynomial helps compute flow growth rates in 3D manifolds.
problem Computing growth rates of pseudo-Anosov flows in 3-manifolds.
method Modified veering polynomial and combinatorial flow graph.
result Computes growth rates of pseudo-Anosov flows after cutting.
Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …
Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.
problem Characterize essential surfaces in Seifert fiber spaces with singular surfaces.
method Extends Frohman and Rannard's approach to handle surfaces with singular fibers.
result Characterizes essential surfaces in Seifert fiber spaces with singular surfaces.
Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.
problem Conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.
method Analysis of GKM graphs and fiber bundles, counterexamples, and classification of twist automorphisms.
result Realizability of fiber bundles of GKM graphs depends on the twist automorphism and can be decided in terms of the classification.
Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
problem Characterize fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
method Construct a class of involutions, extend product involutions, and use double covering.
result Any fiber-preserving, orientation-reversing involution factors as a product of an orientation-preserving and a specific class of involutions.
We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2-knots. As an application, we produce infinite families…
Introduces Darboux-Lie derivative for fiber bundles.
problem None explicitly stated; focuses on introducing a new derivative.
method Study of Darboux-Lie derivative for fiber-bundle maps.
result Properties of Darboux-Lie derivative for fiber bundles.
The paper proves non-existence of positive scalar curvature on certain fiber bundles.
problem The existence of positive scalar curvature metrics on fiber bundles.
method Analyzing fiber bundles over specific manifolds with incompressible or homotopically nontrivial fibers.
result Non-existence of PSC metrics on certain fiber bundles under specific conditions.
New examples show not all homology fiber bundles are topological.
problem Disprove conjecture about homology fiber bundles.
method Construct flat, projective morphisms that are Z-homology fiber bundles. result Disprove conjecture about homology fiber bundles.
New exotic 4-manifolds found with fiber bundles.
problem Finding non-diffeomorphic exotic 4-manifolds.
method Smooth fiber bundles over the circle.
result Exotic 4-manifolds with non-simply-connected fiber.
Study shows simplicial volume of certain fiber bundles is zero.
problem Understanding simplicial volume in fiber bundles with nonpositive curvature.
method Proved simplicial volume is zero for specific fiber bundles.
result Simplicial volume of certain fiber bundles is zero.
The branched virtual fibering theorem by Sakuma states that every closed orientable 3-manifold with a Heegaard surface of genus g has a branched double cover which is a genus g surface bundle over the circle. It is proved by Brooks that such a surface bundle can be chosen to be hyperbolic. We prove that the minim…
We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The (-3,3,5)-pretzel…
We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a characterisation of fibered surfaces with zero signature.
Constructs a family to handle unstable fibers on complex surfaces.
problem Handling unstable fibers on complex surfaces.
method Uses Teichmüller theory to construct a degenerating family over the moduli space.
result Any fibered complex surface with unstable fibers can be pulled back from the constructed family.
The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.
Groups with Property (T) have fiber products with Property (T).
problem When does the fiber product of groups with Property (T) have Property (T)?
method Analyzing fiber products of groups with Property (T).
result Fiber products of groups with Property (T) also have Property (T).
Boundary of fiber convex domains is a cohomological sphere.
problem Understanding the boundary properties of fiber convex domains.
method Analyzing smooth fiber convex domains with smooth boundaries.
result The boundary is a cohomological sphere.
Study complex surfaces fibered over Teichmüller curves with Veech fibers.
problem Understanding the geometric and topological properties of complex surfaces.
method Compute invariants via monodromy action on fiber's mod-m homology. result Exact values of invariants for all known algebraically primitive Teichmüller curves.
In this paper, we define the primitive/Seifert-fibered property for a knot in S^3. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S^2 and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of exa…
Describes 3-manifolds by families of singularly fibered surfaces.
problem Understanding the structure of 3-manifolds through fibered surfaces.
method Explicitly describes a fibration of the complement of a homogeneous braid.
result Each fiber intersects every cross-section of S3. A fibered concordance of knots, introduced by Harer, is a concordance between fibered knots that is well-behaved with respect to the fibrations. We consider semi-fibered concordance of two component ordered links L=J⊔K with J fibered. These are concordances that restrict to fibered concordances on the first …
Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.
problem Characterizing Veech groups in fibered 3-manifolds.
method Analyzing pseudo-Anosov monodromies and foliations, proving properties of Veech groups.
result Veech groups in fibers typically contain no parabolic elements.
Paper connects homologically fibered links to solutions of equations.
problem Existence of homologically fibered links in 3-manifolds.
method Interprets existence in terms of first homology group and torsion linking form, or surgery diagrams.
result Computes hc for specific 3-manifolds.
Defines products for fibered corners manifolds, generalizing resolutions.
problem Resolving fibered corners manifolds.
method Introduces a category of fibered corners manifolds with products and transverse fiber products, defining the 'ordered product' for wedge metrics.
result The 'ordered product' is a natural product for wedge metrics.
Study simplicial volume in fiber bundles with connected groups.
problem Understanding simplicial volume in fiber bundles.
method Investigated fiber bundles with connected structure groups.
result Simplicial volume of total space matches trivial bundle under certain conditions.
New research finds infinitely many hyperbolic knots not almost-fibered.
problem Understanding the properties of knots and their complements.
method Examined hyperbolic knots and their Seifert surfaces.
result Existence of infinitely many hyperbolic genus one knots that are not almost-fibered.
The paper constructs trisections for fiber bundles over a circle.
problem Building trisections for fiber bundles over the circle.
method Using sutured Heegaard splittings and diagrams, the paper provides an algorithm to construct relative trisection diagrams.
result Explicit construction of relative trisection diagrams for fiber bundles over the circle.
Simpler proof for Kielak's virtual fibering criterion.
problem Virtual fibering criterion for RFRS groups
method Simpler proof
result Simplified proof of Kielak's criterion
We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgeries between fibered links and introduce an operation called Generalized Hopf banding. We further characterize generalized crossing changes bet…
Study non-fibered links' relation to tight contact structures.
problem Understanding non-fibered links and their tight contact structures.
method Analyze non-fibered links with induced partial open books and contact structures.
result Strongly quasipositive non-fibered links induce tight contact structures, but the converse is not always true.
Around 1960, R. Palais and J. Cerf proved a fundamental result relating spaces of diffeomorphisms and imbeddings of manifolds: If V is a submanifold of M, then the map from Diff(M) to Imb(V,M) that takes f to its restriction to V is locally trivial. We extend this and related results into the context of fibered manifol…
The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a complete characterization of the stably decomposable torus fiber bundle of fiber-dimens…