A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Divides help construct fibered links from singularities.
The paper extends monodromy theory to incompressible surfaces in 3-manifolds and applies it to link primeness.
We show that there are only finitely many homogeneous links whose Conway polynomial has any given degree. Using this we give an example of an inhomogeneous, fibred knot. Secondly, we show how to compute the monodromy of a homogeneous link complement from a homogeneous braid word representative.
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…
Dualities in deformed N=2 SCFTs from link monodromy on D3-brane states.
New lattices are linked to higher hypergeometric functions.
Study annular concordance invariants and refine transverse link invariants.
Positive braids linked to knot invariants and geometric monodromy groups.
In "Tunnel one, fibered links", the second author showed that the tunnel of a tunnel number one, fibered link can be isotoped to lie as a properly embedded arc in the fiber surface of the link. In this paper, we analyze how the arc behaves under the monodromy action, and show that the tunnel arc is nearly clean, with t…
This paper presents a construction of fibered links out of chord diagrams $\sL$. Let be the incidence graph of $\sL$. Under certain conditions on $\sL$ the symmetrized Seifert matrix of equals the bilinear form of the simply-laced Coxeter system associated to ; and the monodromy of $(K,Σ)…
Alternating-sign Hopf plumbing along a tree yields fibered alternating links whose homological monodromy is, up to a sign, conjugate to some alternating-sign Coxeter transformation. Exploiting this tie, we obtain results about the location of zeros of the Alexander polynomial of the fibered link complement implying a s…
We investigate the local contribution of the braid monodromy factorization in the context of the links obtained by the closure of these braids. We consider plane curves which are arrangements of lines and conics as well as some algebraic surfaces, where some of the former occur as local configurations in degenerated an…
Starting from a divide, i.e. a generic immersion of finitely many copies of the interval [0,1] in the disk, we construct a classical link in the 3-sphere. We prove that the link's complement fibers over the circle, if the divide is connected. Moreover, we compute the monodromy diffeomorphism from the combinatorics of t…
We give a topological model for a polynomial map from $\C^n$ to $\C$ in the neighborhood of a fiber with isolated singularities. This is motivated out of the ``unfolding of links'' described earlier by the first author and Lee Rudolph. The topological model gives a useful encoding of the local and global monodromy for …
Paper connects quantum representations to fibered links and Turaev-Viro invariants.
This paper classifies fibered links in 3-sphere using open book decompositions.
Open books link prime positive braids to checkerboard graphs.
We compute two-term skein modules of framed oriented links in oriented 3-manifolds. They contain the self-writhe and total linking number invariants of framed oriented links in a universal way. The relations in a natural presentation of the skein module are interpreted as monodromies in the space of immersions from cir…
Study vineyards linking TDA and knot theory, showing rich topological features.
A closed braid naturally gives rise to a transverse link in the standard contact 3-space. We study the effect of the dynamical properties of the braid monodromy, such as right-veering, on the contact-topological properties of the transverse link and its transverse invariants in knot Floer and Khovanov homologies. In pa…
New proof shows unique symplectic fillings for certain surface singularity links.
Study symplectic structures on open 4-manifolds with distinct primitive cohomologies.
These are notes from lectures given at the Clay Institute Summer School on "Floer homology, gauge theory and low-dimensional topology" (Budapest, 2004). The first part describes as background some of the geometry of symplectic fibre bundles and their monodromy. The second part, overviewing joint work with Paul Seidel, …
We consider S^1-families of Legendrian knots in the standard contact R^3. We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the starting (and ending) point. We prove this monodromy is a homotopy invariant of the loop. We also establish techniques to address …
Gromov-Witten invariants linked to flat connections and Donaldson-Thomas invariants.
Study on four-dimensional Dehn twists and Milnor fibrations, revealing new phenomena.
The paper studies symplectic operations on Stein fillings of Brieskorn singularities.
The study establishes a link between the complexity of fibered knots and the genus of their Heegaard splittings.
We deduce from a rooted tree in the disk a slalom divide and a slalom knot. A slalom knot is either the local link of a simple plane curve singularity of type A_2n, E_6, E_8 or a fibered hyperbolic knot with very special monodromy.
Positive factorization for pseudoperiodic homeomorphisms on surfaces.
Let be the minimal dilatation for pseudo-Anosovs on a closed surface of genus and let be the minimal dilatation for pseudo-Anosovs on with orientable invariant foliations. This paper concerns the pseudo-Anosovs which occur as the monodromies on closed fibers for Dehn fillings of for…
Given a fibered link, consider the characteristic polynomial of the monodromy restricted to first homology. This generalizes the notion of the Alexander polynomial of a knot. We define a construction, called iterated plumbing, to create a sequence of fibered links from a given one. The resulting sequence of characteris…
The paper shows knots can have zero support genus in certain spaces.
From a fibered link in the 3-sphere may be constructed a field of not everywhere tangent 2-planes; when the fibered link is the link of an isolated critical point of a map from 4-space to the plane, the plane field is essentially the field of kernels of the derivative of the map. Homotopically, such a plane field deter…
For a generic degree d smooth map f: N^n -> M^n we introduce its "transverse fundamental group" π(f), which reduces to π_1(M) in the case where f is a covering, and in general admits a monodromy homomorphism π(f) -> S_{|d|}; nevertheless, we show that π(f) can be non-trivial already for rather simple degree 1 maps S^n …
A divide is a relative generic immersion of a finite union of copies of the unit interval in the unit disk. A divide defines a classical link in the 3- sphere, which is a fibered link if the image of the immersion is connected. We prove in this paper, that the Lefschetz number of the monodromy is 0. This result was kno…
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 of hyperbolic 3-manifolds using gluing equations and torsion.
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show…
This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof of Harer's conjecture on fibred links, construction of symplectic caps to filli…
Whitehead link surgeries are not L-spaces if they support taut foliations.
Curious connection found between dynamical systems and 3D manifold fibrations.
Monodromy groups help test Lie groupoids for faithful representations.
We show that a variety of monodromy phenomena arising in geometric topology and algebraic geometry are most conveniently described in terms of quandle homomorphisms from a knot quandle associated to the base to a quandle associated to a fiber. We consider the cases of the monodromy of a branched covering, braid monodro…
We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the …
Paper studies Lagrangian submanifolds and their homological monodromy.
In this paper we build a link between the Teichmuller theory of hyperbolic Riemann surfaces and isomonodromic deformations of linear systems whose monodromy group is the Fuchsian group associated to the given hyperbolic Riemann surface by the Poincare' uniformization. In the case of a one-sheeted hyperboloid with n orb…
New conditions found for hyperbolic bicycle tracks.