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.
New theory proves infinite homology 3-spheres in homology 4-spheres.
Ancient Ricci flow found from Taub-Bolt metric.
Paper shows Ricci flow with surgery converging to Taub-NUT metric.
Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unital energ…
Solves geodesic equations on specific metrics.
Paper shows perturbed Taub-Bolt metric becomes singularity under Ricci flow.
We propose a construction of Skyrme fields from holonomy of the spin connection of gravitational instantons. The procedure is implemented for Atiyah-Hitchin and Taub-NUT instantons. The skyrmion resulting from the Taub-NUT is given explicitly on the space of orbits of a left translation inside the whole isometry group.…
The paper explores Kähler structures of Taub-NUT and Kerr spaces.
These are notes of lectures given at the NATO Summer School, Montreal 1995. Taubes's recent spectacular work setting up a correspondence between -holomorphic curves in symplectic 4-manifolds and solutions of the Seiberg-Witten equations counts -holomorphic curves in a somewhat new way. The "standard" theory conce…
Study instanton metrics via Taub-NUT deformations.
Instantons on multi-Taub-NUT spaces are mapped to bow representations.
This paper studies the space of harmonic forms and harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find a 2-parameter family of zero mod…
In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and ass…
Researchers found a new 8D Taub-NUT-like metric using harmonic superspace.
Extends Taubes's theorem to non-compact manifolds with harmonic forms.
We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that should be sufficient for blow-up and gluing arguments. In particular we parametrize their geodesics from the origin, determine curva…
This work continues the study of a homotopy-theoretic construction of the author inspired by the Bott-Taubes integrals. Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots. Their techniques were later used by Cattaneo et al. to construct real…
Gravitational instantons are constructed as superpositions of Atiyah-Hitchin and Taub-NUT geometries.
Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.
We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on mult…
Study sequences of solutions to Taubes's Seiberg-Witten equations with unbounded energy.
This paper is motivated by a relatively recent work by Joyce in special Lagrangian geometry, but the basic idea of the present paper goes back to an earlier pioneering work of Donaldson in Yang--Mills gauge theory; Donaldson discovered a global structure of a (compactified) moduli space of Yang--Mills instantons, and a…
We present a construction of self-dual Yang-Mills connections on the Taub-NUT space. We illustrate it by finding explicit expressions for all SU(2) instantons of instanton number one and generic monodromy at infinity.
We study the Hessian geometry of toric multi-Taub-NUT metrics and their phase change phenomena via the images of their moment maps. This generalizes an earlier paper on toric Gibbons-Hawking metrics.
We introduce a generalization of Taub-NUT deformations for large families of hyper-Kaehler quotients including toric hyper-Kaehler manifolds and quiver varieties, and apply them to the case of the Hilbert schemes of k points on C^2.
Ricci flow converges to Taub-NUT metric under specific conditions.
Defines monopole Floer homology for 3-manifolds with toroidal boundaries.
This is an introduction to Taubes's proof of the Weinstein conjecture, written for the AMS Current Events Bulletin. It is intended to be accessible to nonspecialists, so much of the article is devoted to background and context.
New extremal Kähler metrics found on 4-manifolds with U(2) symmetry.
This work shows all conformally Kähler, Ricci-flat toric metrics on non-compact surfaces are known families.
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-N…
It is well known that certain combinations of configuration space integrals defined by Bott and Taubes produce cohomology classes of spaces of knots. The literature surrounding this important fact, however, is somewhat incomplete and lacking in detail. The aim of this paper is to fill in the gaps as well as summarize t…
We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.
We find sufficient conditions for the absence of harmonic spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of…
Constructs an asymptotic metric for moduli space of centred hyperbolic monopoles.
An interesting question in symplectic topology, which was posed by C. H. Taubes, concerns the topology of closed (i.e. compact and without boundary) connected oriented three dimensional manifolds whose product with a circle admits a symplectic structure. The only known examples of such manifolds are those which fiber o…
Complete Calabi-Yau metrics on C^{N+1} are constructed.
Classifies instantons on ALF multi-Taub-NUT spaces and ties them to bow solutions.
Study shows instantons and monopoles decompose into U(1) components.
This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperkähler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard $\rl^3 \times \sph^1$ or a multi-Taub-NUT mani…
The paper proves properties of Kähler surfaces with zero scalar curvature.
We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. W…
In this paper we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L^2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a …
This article finds a structure of singular sets on compact Kahler surfaces, which Taubes introduced in the studies of the asymptotic analysis of solutions to the Kapustin-Witten equations and the Vafa-Witten ones originally on smooth four-manifolds. These equations can be seen as real four-dimensional analogues of the …
In this paper connections between different gauge-theoretical problems in high and low dimensions are established. In particular it is shown that higher dimensional asd equations on total spaces of spinor bundles over low dimensional manifolds can be interpreted as Taubes-Pidstrygach's generalization of the Seiberg-Wit…
Study on eigenfunctions on sphere configurations, proving non-existence and construction of critical eigensections.
Special Lagrangian submanifolds emerge from K3 surface collapse.
The goal of this paper is to give a new proof of a theorem of Meng and Taubes that identifies the Seiberg-Witten invariants of 3-manifolds with Milnor torsion. The point of view here will be that of topological quantum field theory. In particular, we relate the Seiberg-Witten equations on a 3-manifold with the Abelian …