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.
A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in $\wedge^3 \g$ associated to an invariant inner product. We introduce the concept of the fusion for such manifolds, and we relate quasi-Poisson manifolds …
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…
New Lie 2-algebra structure for multiplicative forms on quasi-Poisson groupoids.
We provide a quasi-Poisson version of the Drinfeld's correspondence between Poisson homogeneous spaces and Lagrangian subalgebras.
We reformulate notions from the theory of quasi-Poisson g-manifolds in terms of graded Poisson geometry and graded Poisson-Lie groups and prove that quasi-Poisson g-manifolds integrate to quasi-Hamiltonian g-groupoids. We then interpret this result within the theory of Dirac morphisms and multiplicative Manin pairs, to…
We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.
Study of mixed product Poisson structures on Lie group and bialgebra manifolds.
Develops reduction method for strong Dirac maps.
New constructions and examples from moduli spaces.
A Lie group G in a group pair (D,G), integrating a Lie algebra g in a Manin pair (d,g) has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, that generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are quasi-h…
Shows natural quasi-Poisson structure on multiplicative Grothendieck-Springer space.
Given an oriented surface S with base point * on the boundary, we introduce for all N>0, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of π_1(S,*). Our bracket extends the well-known Poisson bracket on GL_N-invariant functions on this space. Our main tool is a natural structure …
Abstract: Homotopy Poisson algebra models for reduced spaces derived from Poisson structures.
Deform symplectic structures using moment maps and Lie algebra elements.
New Poisson structures defined on surface moduli spaces.
We study Maurer-Cartan elements on homotopy Poisson manifolds of degree . They unify many twisted or homotopy structures in Poisson geometry and mathematical physics, such as twisted Poisson manifolds, quasi-Poisson $\g$-manifolds, and twisted Courant algebroids. Using the fact that the dual of an -term $L_\infty…
We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also that the structures induced on their base manifolds are related via a quasi Poissoniza…
The paper constructs a noncommutative bracket on surface groups and proves it's Hamiltonian.
Using ideas from an article of P. Bieliavsky, M. Rooman and Ph. Spindel on BTZ black holes, I construct a family of interesting examples of quasi-Poisson actions as defined by A. Alekseev and Y. Kosmann-Schwarzbach. As an application, I obtain a genuine Poisson structure on which induces a Poisson structure o…
The paper integrates quasi-Poisson manifolds into multiplicative D-valued moment maps.
We prove the universal lifting theorem: for an -simply connected and -connected Lie groupoid $\gm$ with Lie algebroid , the graded Lie algebra of multi-differentials on is isomorphic to that of multiplicative multi-vector fields on $\gm$. As a consequence, we obtain the integration theorem for a quasi-Lie …
A new double quasi-Poisson bracket on surface groups.
We study Dirac structures associated with Manin pairs (\d,\g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, pro…
Reformulates Fock-Rosly Poisson structure using quasi-triangular r-matrices.
Develops new Poisson structures for moduli spaces.
Let G be a Lie group endowed with a bi-invariant pseudo-Riemannian metric. Then the moduli space of flat connections on a principal G-bundle, P\to Σ, over a compact oriented surface, Σ, carries a Poisson structure. If we trivialize P over a finite number of points on the boundary of Σ, then the moduli space carries a q…
Simplified method for algebra of Dirac structures.
In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures and Poisson groupoid actions naturally appear in this setting. As an application, we use a generalized dynamical r-matrix induced by the gauge fixing procedure to give a new fi…
The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.
We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant algebroid and A\subset E is a Dirac structure. These spaces are defined in terms of morphisms of Courant algebroids with suitable compatibility conditions. Several of their properties are discussed, including a reduction procedure. This set-u…
The paper explores Poisson structures on differentiable stacks, developing new mathematical tools.
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…
This paper is a continuation of [KS]. We develop the results of [KS] principally in two directions. First, we generalize the main result of [KS], the connection between the solutions of the classical dynamical Yang-Baxter equation and Poisson homogeneous spaces of Poisson Lie groups. We hope that now we present this re…
A Dirac structure is a Lagrangian subbundle of a Courant algebroid, , which is involutive with respect to the Courant bracket. In particular, inherits the structure of a Lie algebroid. In this paper, we introduce the more general notion of a pseudo-Dirac structure: an arbitrary subbundle, $W\sub…
Defines Lie and Courant algebroids over Lie groupoids using homological vector fields.
This research extends tetrahedron reconstruction to curved spaces using group-valued moment maps.
New class of metric f-manifolds introduced.
Characterizes and describes selfsimilar Hessian manifolds with homothetic vector fields.
Extends Tian theorem to Vaisman manifolds for approximations.
The paper defines trans-para-Sasakian manifolds and explores their geometric properties.
In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with -dimensional contact metric manifold and this manifold, we have called generalized Kenmotsu manifolds. Necessary and sufficient c…
Study on a new type of manifolds that generalize almost C-manifolds.
New class of complex manifolds defined, properties studied.
Stabilized convex symplectic manifolds are equivalent to flexible Weinstein manifolds.
New criteria for Sasakian manifolds and classification of nearly cosymplectic manifolds.
Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.
Determines the type of 3-manifolds from their covers.
The study identifies criteria for 3-manifolds to be boundaries of exotic 4-manifolds.