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 explores twisted Lagrangian tori in C^2 and their Hamiltonian stationarity.
The paper classifies multiplicity free Hamiltonian actions and quasi-Hamiltonian manifolds.
We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes the quantization of Hamiltonian -spaces to quasi-Hamiltonian…
Study measures invariant DH on twisted moduli spaces.
A closed 3-form defines an extension of by . This fact leads to the definition of the group of -twisted Hamiltonian symmetries $\Ham(M, \JJ; H)$ as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold. The Hamiltonian redu…
Consider an effective Hamiltonian torus action on a topologically twisted,generalized complex manifold of dimension . We prove that the and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying $rank(T) =…
Generalizes isomonodromic-isospectral correspondence for twisted connections.
We explain how to define the quantization of q-Hamiltonian SU(2)-spaces as push-forwards in twisted K-homology, and prove a `quantization commutes with reduction' theorem for this setting. As applications, we show how the Verlinde formulas for flat SU(2) or SO(3) bundles are obtained by localization in twisted K-homolo…
It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology t…
In this paper, we consider generalized moment maps for Hamiltonian actions on -twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness properties for generalized moment maps. We study Hamiltonian torus actions on compact …
We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of the vortex equations and computes the Hamiltonian Gromov-Witten invariants. When t…
Paper proves periodic orbits for Hamiltonian systems in twisted disc bundles.
Classifies compact multiplicity free quasi-Hamiltonian manifolds.
We study generalized moment maps for a Hamiltonian action on a connected compact -twisted generalized complex manifold introduced by Lin and Tolman and prove the convexity and connectedness properties of the generalized moment maps for a Hamiltonian torus action.
Consider the Hamiltonian action of a torus on a compact twisted generalized complex manifold . We first observe that Kirwan injectivity and surjectivity hold for ordinary equivariant cohomology in this setting. Then we prove that these two results hold for the twisted equivariant cohomology as well.
On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points projects onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least de…
The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of hamiltonian and Poisson actions. In this paper, we extend this correspondence to the c…
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian quasi-Poisson manifolds fit into this framework by constructing an ``inversion'' procedur…
We construct $\sorth{p} \times \sorth{q}$-invariant special Lagrangian (SL) cones in $\C^{p+q}$. These SL cones are natural higher-dimensional analogues of the $\sorth{2}$-invariant SL cones constructed previously by MH and used in our gluing constructions of higher genus SL cones in $\C^{3}$. We study in detail the ge…
New K-theoretic invariants for Hamiltonian fibrations discovered.
The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical manifold carry contractible periodic orbits of the Hamiltonian flow, provided th…
New methods prove non-squeezing in locally conformal symplectic geometry.
We describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern-Weil homomorphism to the twisted equivariant cohomology. We clarify that in order to have a cohomology theory, the coefficients of the twisted equivariant cohomology must…
The paper connects twist and modification methods to build hyperKähler structures.
The paper studies LCS bundles and conditions for their total spaces to have LCS forms.
In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of the fixed global extrema in the Floer complex of the generating Hamiltonian. Our…
It has been shown recently that extended supersymmetry in twisted first-order sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions relating the twisted generalized complex structure and the geometrical data defining…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin-complex under consideration is allowed to be further twisted by certain natural exterior power bundles. The main result is a weighted quantization formula in the presence…
The Hamiltonian flow of the standard metric Hamiltonian with respect to the twisted symplectic structure on the cotangent bundle describes the motion of a charged particle on the base. We prove that under certain natural hypotheses the number of periodic orbits on low energy levels for this flow is at least the sum of …
Study shows bi-Hamiltonian structure for polygon evolutions in centro-affine space.
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula i…
We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group on a Poisson manifold , we find an explicit description of the lifted hamiltonian act…
Let G be a compact, simply connected Lie group. We develop a `quantization functor' from pre-quantized quasi-Hamiltonian G-spaces at level k to the fusion ring (Verlinde algebra) R_k(G). The quantization Q(M) is defined as a push-forward in twisted equivariant K-homology. It may be computed by a fixed point formula, si…
We show that if K: P \to R is an autonomous Hamiltonian on a symplectic manifold (P,Ω) which attains 0 as a Morse-Bott nondegenerate minimum along a symplectic submanifold M, and if c_1(TP)|_M vanishes in real cohomology, then the Hamiltonian flow of K has contractible periodic orbits with bounded period on all suffici…
Given a submersion with an Ehresmann connection , we describe how to solve Hamiltonian systems on by lifting our problem to . Furthermore, we show that all solutions of these lifted Hamiltonian systems can be described using the original Hamiltonian vector field on along with a gener…
New probabilistic constructions for Kähler-Einstein metrics.
Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics relative to such braid classes and define a braid Floer homology. This refinement of t…
Extends moment map concept to locally conformally Kähler manifolds.
In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is L…
The abstract investigates convexity in locally conformally symplectic geometry.
The paper defines a ring structure in twisted equivariant -theory for Lie groups.
The SL(2)-character variety X of a closed surface M enjoys a natural complex-symplectic structure invariant under the mapping class group G of M. Using the ergodicity of G on the SU(2)-character variety, we deduce that every G-invariant meromorphic function on X is constant. The trace functions of closed curves on M de…
These notes discuss various aspect of the ``representation theory'' of Poisson manifolds, with focus on Morita equivalence and Picard groups. We give a brief introduction to Poisson geometry (including Dirac and twisted Poisson structures) and algebraic Morita theory before presenting the geometric Morita theory of Poi…
We considered a surgery, called Lagrangian attaching disk surgery, that can be applied to a Lagrangian surface L at the presence of a Lagrangian attaching disk D, to obtain a new Lagrangian surface L' which is always smoothly isotopic to L. We showed that this type of surgery includes all even generalized Dehn twists a…
The article studies Hamiltonian flows on surface group representations induced by invariant multi-functions.
Defines operations in generalized complex geometry and applies them to deform and relate Kahler metrics.
The paper connects isomonodromic and isospectral deformations for connections.
SU(n)-structures derived from Kähler manifolds with torus actions.