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).
Survey on algebraic fibers of group extensions and their finiteness properties.
problem Existence and finiteness of algebraic fibers in group extensions.
method Analysis of abstract and pro-p groups. result Finiteness properties of algebraic fibers in group extensions.
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…
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.
It is shown, using sutured manifold theory, that if there are any 2-component counterexamples to the Generalized Property R Conjecture, then any knot of least genus among components of such counterexamples is not a fibered knot. The general question of what fibered knots might appear as a component of such a counterexa…
The study explores how surface diffeomorphisms of knots relate to their topological properties.
problem Understanding how properties of surface diffeomorphisms of knots relate to their topological properties.
method Examining both braid and fibered knot perspectives to explore the relationship between surface diffeomorphisms and knot properties.
result Properties of surface diffeomorphisms may relate to four-dimensional topological properties of knots, such as the slice genus.
Collects properties of Seifert homology spheres for concordance studies.
problem Understanding concordance properties of fibers in Seifert homology spheres.
method Using Dehn surgery along Seifert fibers.
result Includes various properties in one place for concordance studies.
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…
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.
The paper studies topological indices of geometric operators on manifolds with fibered boundaries.
problem Investigating indices of geometric operators on manifolds with fibered boundaries.
method Defining K-groups relative to pushforward for boundary fibration, using groupoid deformation techniques to prove properties of indices.
result Indices of twisted geometric operators can be understood as index pairings over K-groups.
This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.
problem Theoretical development of property inheritance for subtensors in tensor train decompositions.
method Theoretical analysis of incoherence and condition number preservation, and tensor train rank preservation through fiber-wise sampling.
result Key tensor properties (incoherence and condition number) can be well preserved to subtensors formed via fiber-wise sampling.
Constructs examples of complex 3D shapes with specific properties.
problem Creating fibered three-manifolds with certain characteristics.
method Builds examples using handlebody bundles and polytopes.
result Examples of fibered three-manifolds with specific properties.
Bi-orderable groups from left-orderable ones, showing non-profinite properties.
problem Non-profinite properties in bi-orderability and generalized torsion elements.
method Using fiber products to construct bi-orderable groups, showing non-profinite properties.
result Bi-orderability and generalized torsion elements are not profinite properties.
New knot found with unique property.
problem Existence of hyperbolic fibered slice knots with specific monodromy.
method Constructed a specific type of hyperbolic fibered slice knot.
result Negative answer to a question posed by Hubbard et al.
If there are any 2-component counterexamples to the Generalized Property R Conjecture, a least genus component of all such counterexamples cannot be a fibered knot. Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions. The simplest plausible counterexample to the Gene…
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.
We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of "extremal" tight contact structures. Specifically, there is exactly one contact s…
Study Poisson structures on fibered 5-manifolds with compatibility conditions.
problem Understanding Poisson structures on fibered 5-manifolds.
method Using almost coupling condition and bigraded factorization of the Jacobi identity.
result Describe global behavior and singularities of almost coupling Poisson tensors.
Study of new link types and their invariants, extending previous results.
problem Properties of polynomial invariants and signatures of weakly successively almost positive links.
method Analysis of minimal genus and fibering properties, extending known theorems.
result Extension of Scharlemann-Thompson's theorem to weakly successively almost positive links.
This work concerns stability and instability of Einstein warped products with an Einsteinian fiber of codimension 1. We study the cases where the scalar curvature of the warped product and of the fiber are either both positive or both negative to complement the results in [Krö16]. Up to a small gap in the case of sin-c…
In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of SO(4), this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3…
Study pseudo-Anosov monodromies in fibered 3-manifolds using asymptotic translation lengths.
problem Understanding the normal generation of pseudo-Anosov monodromies in fibered 3-manifolds.
method Using asymptotic translation lengths on the curve complex and analyzing properties of sequences of fibers and monodromies.
result For most primitive integral classes, pseudo-Anosov monodromies normally generate the mapping class group on the fiber surface.
Study on spectral properties of Riemannian submersions with special fibers.
problem Analyzing spectral properties of Riemannian submersions with fibers of basic mean curvature.
method Comparing the spectrum of the total space with a Schrödinger operator on the base manifold, extending results on Riemannian coverings.
result Computed the bottom of the spectrum and Cheeger constant for connected, amenable Lie groups.
Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups-so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then p…
The paper studies fibering properties of RACGs and random subcomplexes of buildings.
problem Higher virtual algebraic fibering properties of right-angled Coxeter groups.
method Generalization of Bestvina-Brady discrete Morse theory applied to Davis complex, combined with probabilistic arguments.
result Commutator subgroups of RACGs with certain finite building flag complexes admit epimorphisms to Z with strong topological finiteness properties.
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-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber …
The paper studies mapping class groups of nontrivial S2 fiber bundles.
problem Analyzing the mapping class groups of nontrivial S2 fiber bundles. method Using generalizations of Dax invariants for embedded surfaces in 4-manifolds.
result Surjective homomorphisms from MCG(X) and MCG(X′) to Z∞ are shown. 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…
Introduces cofrontal mappings and studies their properties.
problem Understanding the properties and behavior of cofrontal mappings.
method Study of cofrontal mappings' local and global properties, construction of fair cofrontals, and classification.
result Cofrontal mappings are very special and restrictive, but can be approximated by fair ones.
Machine learning optimizes polymer fiber synthesis.
problem Complex material synthesis requires impractical experimentation.
method Bayesian optimisation using machine learning.
result Efficiently directs synthesis to achieve material and process objectives.
The paper explores properties of LCK spaces and their coverings.
problem Understanding the structure and properties of LCK spaces and their coverings.
method Proving that a space is LCK if and only if its universal cover is Kähler, and showing that a complex space with discrete fibers over an LCK space also has an LCK structure.
result Spaces with discrete fibers over LCK spaces also have LCK structures.
In a recent paper, Dimca and Nemethi pose the problem of finding a homogeneous polynomial f such that the homology of the complement of the hypersurface defined by f is torsion-free, but the homology of the Milnor fiber of f has torsion. We prove that this is indeed possible, and show by construction that, for each pri…
We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres with the property that every commensurable knot complement in a homology sphere has non-monic…
Homotopy equivalence found between Milnor-Lê fibers of specific singularities.
problem Analyzing non-isolated singularities and their Milnor-Lê fibers.
method Using transversality property and homotopy equivalence to relate Milnor-Lê fibers of different singularities.
result Homotopy equivalence between negative Milnor-Lê fibers of specific singularities.
We introduce two K-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these K-theories, and construct a natural homomorphism from the VOA K-theory to the associa…
Paper investigates double coverings and torsions in homology groups.
problem Relationship between cohomology ranks and twisted cohomology groups.
method Analyzes double coverings and torsions in homology groups of Milnor fiber.
result Strict version of Papadima-Suciu's inequality and non-trivial 2-torsion in homology are equivalent.
For a Riemannian submersion from a simple compact Lie group with a bi-invariant metric, we prove the action of its holonomy group on the fibers is transitive. As a step towards classifying Riemannian submersions with totally geodesic fibers, we consider the parameterized surface induced by lifting a base geodesic to po…
The study proves properties of spectral selectors for contact manifolds and applies them to contact big fibers and geodesics.
problem Properties of spectral selectors for contact manifolds.
method Algebraic properties of spectral selectors for strongly orderable contact manifolds.
result Established contact big fiber theorem and constructed norms on contactomorphism group universal cover.
The study bounds and characterizes surfaces containing smooth conics and twistor fibers in a flag threefold.
problem Bounding and characterizing surfaces containing smooth conics and twistor fibers in a flag threefold.
method Analyzing the family of smooth conics and using algebraic properties to construct surfaces.
result The only smooth cases of surfaces containing infinitely many twistor fibers are of bidegree (1,1).
Study essentiality and simplicial volume of manifolds fibered over spheres.
problem When manifolds fibered over spheres are essential or have positive simplicial volume.
method Analyzing mapping tori and fiber bundles over spheres, using results on macroscopic dimension and characteristic classes.
result Mapping tori of odd-dimensional manifolds with non-zero simplicial volume are essential, while fiber bundles over spheres of dimension d > 1 have zero simplicial volume.
New knot homologies detect non-fibered knots, expanding on previous results.
problem Detecting non-fibered knots using knot homologies.
method Developed new knot homologies (knot Floer, Khovanov, HOMFLY) and proved a technical theorem.
result New homologies detect infinitely many non-fibered knots, expanding on previous results.
Classifies certain 3D knots with specific properties.
problem Classifying knots with specific clasp numbers and properties.
method Examined knots with clasp number 2 and genus 2 fibered, using clasp disks of type II.
result Found a partial classification of these knots.
A locally conformally symplectic (LCS) form is an almost symplectic form ω such that a closed one-form θ exists with dω=θ∧ω. A fiber bundle with LCS fiber (F,ω,θ) is called LCS if the transition maps are diffeomorphisms of F preserving ω (and hence θ). In this paper, we find conditions for the total…
New proof shows L-space knots are fibered and have specific properties.
problem Proving L-space knots are fibered and have strong quasipositive properties.
method Conceptually simpler proof using Heegaard Floer homology, translated to instanton Floer homology.
result Generalization of L-space knot properties to other Floer homologies.
A metric space M us said to have the fibered approximation property in dimension n (br., M∈FAP(n)) if for any ε>0, m≥0 and any map g:Im×In→M there exists a map g′:Im×In→M such that g′ is ε-homotopic to g and dimg′({z}×In)≤n for all $z\i…
Fibered knots and disks extend fibrations in 4D space.
problem Extending fibrations from knot complements to disk complements.
method Constructing movies of singular fibrations and identifying sufficient conditions.
result Fibrations extend when disks have exactly two local minima.
Heinz Hopf's famous fibrations of the 2n+1-sphere by great circles, the 4n+3-sphere by great 3-spheres, and the 15-sphere by great 7-spheres have a number of interesting properties. Besides providing the first examples of homotopically nontrivial maps from one sphere to another sphere of lower dimension, they all share…
We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3-sphere is bi-orderable, then its Alexander polynomial has at least one positive real root. Our argument can be applied for a finitely generated group which is an HNN extension with certain propert…