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.
This work classifies monodromy in vineyards using singularity theory.
This paper generalizes monodromy maps for projective structures with poles.
Arithmetic Kontsevich-Zorich monodromy found in a specific origami surface.
Study establishes monodromy equivalence for Lamé-type equations and constructs cone spherical metrics.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
Positive braids linked to knot invariants and geometric monodromy groups.
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…
Paper studies Lagrangian submanifolds and their homological monodromy.
The paper studies transformations of Frobenius manifolds and their properties.
New conditions found for hyperbolic bicycle tracks.
Noninjective monodromy found in polynomial critical point tracking.
We give a systematic method to calculate some homological data from the global monodromy of a topological elliptic surface. We apply this method to the cases 1) the transcendental lattice of an extremal elliptic K3 surface, 2) the torsion part of Mordell-Weil group of a general elliptic surface, and 3) the Mordell-Weil…
The study finds arithmetic groups often in square-tiled surface monodromies.
Characterizes conical angles for metrics with dihedral symmetry.
The geometric monodromy of a plane curve singularity is a quasi-finite diffeomorphism. In this paper we locate the reduction curves of the geometric monodromy and the quadratic vanishing cycles of the singularity. An application to the geometric monodromy group is given.
For any topological groupoid G and any homomorphism from a locally compact Hausdorff topological group K to G, we construct an associated monodromy group. We prove that Morita equivalent topological groupoids have the same monodromy groups. We show how the monodromy groups can be used to test if a Lie groupoid lacks fa…
Study of monodromy and vanishing cycles for complete intersection curves.
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural re…
In this work we describe a method to reconstruct the braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting, since it combines two techniques, namely, the reconstruction of a highly non-generic braid monodromy with a systematic method to go from a non-generic to a generic braid monodro…
The paper studies the index of a specific monodromy for origamis in a particular stratum.
Polynomials with distinct critical values have braid monodromy groups equal to braid groups.
The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot; however, in full generality it is proven only for zeta functions associated to a polynomial in two variables. In this article we consider zeta…
We consider spaces of plane curves in the setting of algebraic geometry and of singularity theory. On one hand there are the complete linear systems, on the other we consider unfolding spaces of bivariate polynomials of Brieskorn-Pham type. For suitable open subspaces we can define the bifurcation braid monodromy takin…
Holomorphic connections found on Riemann surfaces with Fuchsian monodromy.
We outline the construction of the holonomy groupoid of a locally Lie groupoid and the monodromy groupoid of a Lie groupoid. These specialise to the well known holonomy and monodromy groupoids of a foliation, when the groupoid is just an equivalence relation.
Study shows hyperbolic knots' monodromy without fixed points.
In this paper we consider completed coverings that are branched coverings in the sense of Fox. For completed coverings between PL manifolds we give a characterization of the existence of a monodromy representation and the existence of a locally compact monodromy representation. These results stem from a characterizatio…
New knot found with unique property.
Study shows monodromy kernels are large, failing to prove commensurability in specific strata.
New conditions ensure surface group extensions are non-positively curved.
Researchers use Mellin-Barnes integrals to study trinomial equations and their braids.
Axis bundles in free-by-cyclic groups have non-generic monodromies.
We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.
The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendibility of local Lie morphisms.
By a construction of Berstein and Edmonds every proper branched cover f between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of f to the target manifold. For proper branched covers between 2-manifolds the monodromy space i…
Study fibrations over with same singularities, showing monodromies are equivalent up to direct sums.
In this paper we construct effective invariants for braid monodromy of affine curves. We also prove that, for some curves, braid monodromy determines their topology. We apply this result to find a pair of curves with conjugate equations in a number field but which do not admit any orientation-preserving homeomorphism.
Authors construct symplectic Lefschetz pencils on complex projective plane.
Study the monodromy and center-focus problems for rational maps defined by products of generic lines.
Study of translation covers of platonic solids reveals monodromy group structures.
For isolated complex hypersurface singularities with real defining equation we show the existence of a monodromy vector field such that complex conjugation intertwines the local monodromy diffeomorphism with its inverse. In particular, it follows that the geometric monodromy is the composition of the involution induced…
We bound the index of a subgroup in iterated Kodaira fibrations.
New groups discovered with unique properties in a specific space.
Divides help construct fibered links from singularities.
We show that all the currently known non-arithmetic lattices in are monodromy groups of higher hypergeometric functions.
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective ho…
Characterizes monodromies of projective structures on finite-type surfaces.
We give a Lie-theoretic explanation for the convex polytope which parametrizes the globally smooth solutions of the topological-antitopological fusion equations of Toda type (tt-Toda equations) which were introduced by Cecotti and Vafa. It is known from [GL] [GIL1] [M1] [M2] that these solutions can be parametrized…