arXiv research

Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.

Study simplicial volume in fiber bundles with connected groups.

Groups with Property (T) have fiber products with Property (T).

Simpler proof for Kielak's virtual fibering criterion.

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…

We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms …

Survey on algebraic fibers of group extensions and their finiteness properties.

Study shows certain subgroups of fibered 3-manifolds are convex cocompact.

Closed self-covering manifolds with abelian fundamental groups fiber over tori.

A 5-manifold fibers over a circle with nonpositive curvature.

Paper connects homologically fibered links to solutions of equations.

The paper classifies reversible elements in Seifert-fibered spaces and braid groups.

Study of first homology group of Milnor fiber boundary for generic hyperplane arrangements in C^3.

Finite quotients of fibered hyperbolic 3-manifold groups detect taut polynomials.

The paper proves conditions for self-covering manifolds to be fiber bundles over a circle.

The study shows a way to represent Seifert fiber space groups with a limited field size.

Given a manifold M, it is natural to ask in how many ways it fibers (we mean fibering in a general way, where the base might be an orbifold -- this could be described as Seifert fibering)There are group-theoretic obstructions to the existence of even one fibering, and in some cases (such as Kahler manifolds or three-di…

The paper studies elliptic surfaces and proves unique fibered structures.

We define and discuss a notion called fibered commensurability of outer automorphisms of free groups. This notion lets us study symmetry of outer automorphisms. The notion of fibered commensurability is first defined by Calegari-Sun-Wang on mapping class groups. The Nielsen-Thurston type of mapping classes is a commens…

Study of Einstein structures for surface group representations in specific Lie groups.

On a fiber bundle without structure group the action of the gauge group (the group of all fiber respecting diffeomorphisms) on the space of (generalized) connections is shown not to admit slices.

New trick builds hyperbolic manifolds from compact ones, proving some don't virtually fiber.

The paper studies mapping class groups of nontrivial $S^2$ fiber bundles.

Paper constructs hyperbolic Coxeter groups that virtually fiber over Z.

Introduces generalized principal bundles and connections, linking them to standard gauge theories.

Study shows quotient group is infinitely generated.

Surjectivity of Cannon-Thurston map proven for metric graph bundles.

Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over non-free groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every free group of rank at …

Study plane curve singularities to determine vanishing cycles and monodromy groups.

For each g > 2 and h > 1, we explicitly construct (1) fiber sum indecomposable relatively minimal genus g Lefschetz fibrations over genus h surfaces whose monodromies lie in the Torelli group, (2) fiber sum indecomposable genus g surface bundles over genus h surfaces whose monodromies are in the Torelli group (provided…

Paper finds infinite pairs of fiber-type curves with same topology but different embeddings.

Proves 3-manifold groups uniquely identify hyperbolic bundles.

New groups found that don't virtually algebraically fiber, related to mapping class group orbits.

We prove a representation stability result for the Milnor fiber associated to the pure braid group. Our result connects previous work of Simona Settepenella to representation stability in the sense of Church--Ellenberg--Farb, answering a question of Graham Denham. We also use our result to compute the stable integral h…

Calegari's 4-spheres from fibered knots are proven standard.

We consider a homogeneous fibration $G/L \to G/K$, with symmetric fiber and base, where $G$ is a compact connected semisimple Lie group and $L$ has maximal rank in $G$. We suppose the base space $G/K$ is isotropy irreducible and the fiber $K/L$ is simply connected. We investigate the existence of $G$-invariant Einstein…

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class …

Let X be a hyperbolic surface and H the fundamental group of a hyperbolic 3-manifold that fibers over the circle with fiber X. Using the Birman exact sequence, H embeds in the mapping class group Mod(Y) of the surface Y obtained by removing a point from X. We prove that a subgroup G in H is convex cocompact in Mod(Y) i…

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…

The paper constructs moduli spaces for genus one fibered K3 surfaces.

This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds $M$ that fiber over a non-orientable base space. An orientable base space double cover $\tilde{M}$ of $M$ is constructed and then an isomorphism be…

Let $p$ be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually $p$. Let $M=M^3$ be a virtually fibered 3-manifold. It is well-known that $G=π_1(M)$ is residually solvable and even residually finite solvable. We prove that $G$ is always virtually residually $p$…

In this paper, we give some necessary and sufficient conditions for a normal subgroup of an amalgamated product of groups to be finitely generated. We apply these conditions together with Stallings' fibering theorem to prove that an irreducible multilink in a homology 3-sphere fibers if and only if each of its multilin…

Proves incoherence of free-by-free and surface-by-free groups, solving two problems.

Theorems prove upper bounds for foliations on closed Alexandrov spaces.

New gradient Ricci solitons found via fiber bundles.

We consider certain type of fiber bundles with odd dimensional compact contact base, exact symplectic fibers, and the structure group contained in the group of exact symplectomorphisms of the fiber. We call such fibrations "contact symplectic fibrations". By a result of Hajduk-Walczak, some of these admit contact struc…

We introduce generalized arrow diagrams and generalized Reidemeister moves for diagrams of links in Seifert fibered spaces. We give a presentation of the fundamental group of the link complement. As a corollary we are able to compute the first homology group of the complement and the twisted Alexander polynomials of th…