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.
Holomorphic Poisson structures on nilmanifolds have degenerate spectral sequences.
Study BV operators on holomorphic polyvector fields on toric varieties.
Paper describes holomorphic polyvector fields on toric varieties.
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is that it is based on the use of covariant tensors unlike Kontsevich's original p…
The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its non-linear cohomology.
The paper explores Poisson structures on differentiable stacks, developing new mathematical tools.
The paper extends formality and Duflo theorems to Lie pairs, including complex manifolds and foliations.
A class of Z_2-graded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated. They have the form g = g_0 + g_1, with g_0 = so(V) + W_0 and g_1 = W_1, where the algebra of generalized translations W = W_0 + W_1 is the maximal solva…
Defines lift of partial cohomological field theories and finds new bi-Hamiltonian structures.
Formality theorem established for g-manifolds, relating cohomologies of polyvector fields.
We prove a 2-categorical analogue of a classical result of Drinfeld: there is a one-to-one correspondence between connected, simply-connected Poisson Lie 2-groups and Lie 2-bialgebras. In fact, we also prove that there is a one-to-one correspondence between connected, simply connected quasi-Poisson 2-groups and quasi-L…
The paper studies formal geometry of dg manifolds and proves isomorphism of their calculi.
New models for B-type topological theories using complex functions.
Authors find a Hodge-type decomposition for holomorphic Poisson cohomology on nilmanifolds.
Authors prove de Rham cohomology of Poisson and Jacobi manifolds is trivial.
Vector fields invariant under Lie group action are finitely generated by polynomial fields.
The paper classifies invariant structures on complex almost Abelian groups.
New method to determine parabolic surfaces invariant under Killing fields.
The paper extends arithmetic Chern-Simons invariants to real quadratic fields and calculates mod 2 Dijkgraaf-Witten invariants.
Study anti-invariant Riemannian submersions from Kenmotsu to Riemannian manifolds.
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when w…
New invariant 'trunkenness' for 3D volume-preserving vector fields.
New invariants for 3-manifolds from foliations and noncommutative geometry.
Study on vector fields on Lie groups reveals surprising algebraic coincidences.
New field invariant refines real spectrum and relates to absolute Galois group.
Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …
We define an invariant of rational homology 3-spheres via vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant and that of Watanabe's Morse homotopy invariant, which implies the equivalence of these two invariants.
We give a complete list of those left invariant unit vector fields on three-dimensional Lie groups with the left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group with the Sasaki metric. As a result, each class of three-dimensional Lie groups admits the totally geodesic…
Observable structures of a topological field theory of AKSZ type are analyzed. From a double (or multiple) complex structure of observable algebras, new topological invariants are constructed. Especially, Donaldson polynomial invariants and their generalizations are constructed from a topological field theory of AKSZ t…
New method finds algebraic invariants for hyperbolic surfaces.
Defines observer-invariant time derivatives on moving surfaces.
In this paper we consider simply connected Lie groups equipped with left invariant Randers metrics which arise from left invariant Riemannian metrics and left invariant vector fields. Then we study the intersection between automorphism and isometry groups of these spaces. Finally it has shown that for any left invarian…
Study identifies specific subvarieties in translation surfaces with quadratic field.
We call a connected Lie group endowed with a left-invariant Lorentzian flat metric Lorentzian flat Lie group. In this Note, we determine all Lorentzian flat Lie groups admitting a timelike left-invariant Killing vector field. We show that these Lie groups are 2-solvable and unimodular and hence geodesically complete. M…
Topological field theory computes Arf invariant of r-spin surfaces.
We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of . More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field. As an application, we determine the asymptotic Alexander…
Study topological invariants for hypersurfaces using vector fields.
We consider the general nonvanishing, divergence-free vector fields defined on a domain in three space and tangent to its boundary. Based on the theory of finite type invariants, we define a family of invariants for such fields, in the style of Arnold's asymptotic linking number. Our approach is based on the configurat…
We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable endomorphism field . For the normal case, we prove that a -invariant submanifold tangent to a Reeb vector field and orthogonal to the other one is minimal. For a -invariant submanifold everyw…
Residue formula for a complex invariant on orbifolds.
Removes singularities for Yang-Mills-Higgs fields in higher dimensions.
We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, called linear saddle invariants, include many concordance invariants and generate an infinite-dimensional vector space of link invariants. In con…
Study projective symmetries in Finsler spaces, showing reductions and constant flag curvature.
The study explores harmonic vector fields on a specific type of Riemannian Lie group.
A solution of a problem by V.I.Arnol'd about higher analog of the asymptotic Hopf invariant of divergence-free vector fields is presented. A higher invariant of magnetic fields, which is not expressed from the asymptotic linking numbers of magnetic lines is constructed and examples of an asymptotic invariants is constr…
Study spectral invariants over integers, discovering unboundedness and field-dependence.
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the second order. A result on the characterization of classes of these equations by t…
Defines a map from hypersurfaces to spheres using vector fields, linking curvature and topological invariants.