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 paper derives formulas for Chern classes of triangulated circle bundles using combinatorial necklaces.
The paper defines cyclic sets from ribbon string links and connects them to quantum invariants.
This paper generalizes a topological invariant to cyclic Higgs bundles.
We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is cocompact, we develop a generalized Hodge theory for the de Rham cohomology of inv…
New Heegaard Floer homology for orbifolds with cyclic singularities.
Study connects group invariants through outer automorphisms and polynomial relations.
A nonpolycyclic nilpotent-by-cyclic group Gamma can be expressed as the HNN extension of a finitely-generated nilpotent group N. The first main result is that quasi-isometric nilpotent-by-cyclic groups are HNN extensions of quasi-isometric nilpotent groups. The nonsurjective injection defining such an extension induces…
New link invariant bounds topological slice genus.
New formula counts triangles to compute first Chern class of circle bundles.
Study of cyclic pursuit on compact manifolds, conjecturing finite or convergent loops.
Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and solvable cases are studied. We extend to the general case, Kowalski-Tricerri's and Bieszk…
Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev link invariant construction to tangles with a flat connection in a principal G-bundle over the complement of the tangle. The purpose of this paper is to adapt and renormalize their construction to define invariants of G-links using the semi-cyc…
New criteria for splitting definite 4-manifolds with cyclic groups.
The Hodge series of a finite matrix group is the generating function for invariant exterior forms of specified order and degree. Lauret, Miatello, and Rossetti gave examples of pairs of non-conjugate cyclic groups having the same Hodge series; the corresponding space forms are isospectral for the Laplacian on p-forms f…
We produce infinite families of exotic actions of finite cyclic groups on simply connected smooth 4-manifolds with nontrivial Seiberg-Witten invariants.
Given a TQFT in dimension d+1, and an infinite cyclic covering of a closed (d+1)-dimensional manifold M, we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams' work in symbolic dynamics. The Turaev-Viro module associated to…
We prove that on closed Riemannian manifolds with infinite abelian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true if the fundamental group is infinite cyclic. We also formulate a generalization …
The paper presents a chain complex for 3-manifold covers, including surface bundles and surgeries.
Algorithm decides homeomorphism of 4-manifolds.
Survey recent constructions of cyclic cocycles for Lie groups.
We prove a cyclic cohomological analogue of Haefliger's van Est-type theorem for the groupoid of germs of diffeomorphisms of a manifold. The differentiable version of cyclic cohomology is associated to the algebra of transverse differential operators on that groupoid, which is shown to carry an intrinsic Hopf algebraic…
On a smooth closed oriented -manifold with a smooth action of a finite group on a Spin structure, -monopole invariant is defined by "counting" -invariant solutions of Seiberg-Witten equations for any -invariant Riemannian metric on . We compute -monopole invariants on some -manifolds. F…
Algorithms compute invariants of 4-manifolds as branched covers.
Formula for a 3D invariant in contact geometry.
Computes constants for cyclic covers of translation surfaces.
New knot concordance invariants from cyclic covers of prime power.
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the form is parallel. We then describe the structure of the fundamenal group of such m…
We prove a Godbillon-Vey index formula for longitudinal Dirac operators on a foliated bundle with boundary; in particular, we define a Godbillon-Vey eta invariant on the boundary-foliation; this is a secondary invariant for longitudinal Dirac operators on type-III foliations. Moreover, employing the Godbillon-Vey index…
We consider Lie groups equipped with a left-invariant cyclic Lorentzian metric. As in the Riemannian case, in terms of homogeneous structures, such metrics can be considered as different as possible from bi-invariant metrics. We show that several results concerning cyclic Riemannian metrics do not extend to their Loren…
This paper describes cyclic Riemannian Lie groups and their curvatures.
Study integrable discretizations of cyclic systems with circular coordinate lines.
The study broadens the concept of cyclic polytopes to Veronese polytopes.
This work identifies a class of moves on knots which translate to -equivalences of the associated -fold branched cyclic covers, for a fixed and any (with respect to the Goussarov-Habiro filtration.) These moves are applied to give a flexible (if specialised) construction of knots for which the Casson-Walk…
The paper studies norms and invariants for free-by-cyclic groups.
Proves almost profinite rigidity for certain free-by-cyclic groups.
New methods compute Alexander polynomials for complex knots.
In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.
This paper demonstrates a topological meaning of quandle cocycle invariants of links with respect to finite connected quandles , from a perspective of homotopy theory: Specifically, for any prime which does not divide the type of , the -torsion of this invariants is equal to a sum of the colouring po…
T. Mochizuki determined all 3-cocycles of the third quandle cohomologies of Alexander quandles on finite fields. We show that all the 3-cocycles, except those of 2-cocycle forms, are derived from group 3-cocycles of a meta-abelian group. Further, the quandle cocycle invariant of a link using Mochizuki's 3-cocycle is eq…
Geometric formula derived for Lefschetz pairing on Γ-proper manifolds.
Study integral simplicial volume of cyclic covers of torus bundles.
Researchers solve word and conjugacy problems for a specific group family.
Updated rerefences and introduction. Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we give a formula for the the Casson-Walker invariants of these 3-manifolds in terms …
Automorphisms of free groups yield invariant posets of lamination orbits.
Researchers create explicit Hopf cyclic cohomology classes for a specific Hopf algebra.
New quantum invariant is asymptotically multiplicative under cyclic covers.
In this paper, we define finite type invariants for cyclic equivalence classes of nanophrases and construct the universal ones. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold's basic invariants to signed words are finite type invar…