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.
Unified proof of four Bavard dualities and new results on quasimorphisms.
Establishes a duality theorem connecting quasimorphisms and commutator lengths in group theory.
Bavard proved a duality theorem between commutator length and quasimorphisms. Burago, Ivanov and Polterovich introduced the notion of a conjugation-invariant norm which is a generalization of commutator length. Entov and Polterovich proved that Oh-Schwarz spectral invariants are subset-controlled quasimorphisms which a…
Duality result connects bounded cohomology to relative Gromov seminorm.
We prove that for any euclidean ring R and n at least 6, Gamma=SL_n(R) has no unbounded quasi-homomorphisms. From Bavard's duality theorem, this means that the stable commutator length vanishes on Gamma. The result is particularly interesting for R = F[x] for a certain field F (such as the field C of complex numbers, b…
New proof shows lower bound for commutator length in RAAGs.
Study on shortest arcs on hyperbolic surfaces with boundary.
A compact manifold is called Bieberbach if it carries a flat Riemannian metric. Bieberbach manifolds satisfy an isosystolic inequality by a general and fundamental result of M. Gromov. In dimension 3, there exist four classes of non-orientable Bieberbach manifolds up to an affine diffeomorphism. In this paper, We prove…
Survey on invariant quasimorphisms and their relation to stable commutator length.
We study the injectivity radius of complete Riemannian surfaces (S,g) with curvature |K(g)| bounded by 1. We show that if S is orientable with nonabelian fundamental group, then there is a point p in S with injectivity radius at least arcsinh(2/\sqrt{3}). This lower bound is sharp independently of the topology of S. Th…
Given a hyperelliptic Klein surface, we construct companion Klein bottles. Bavard's short loops on companion bottles are studied in relation to the surface to improve an inequality of Gromov's in systolic geometry.
New loxodromic elements found in infinite-type surfaces.
The paper proves optimal systolic inequalities for Möbius strip and Klein bottle.
Stable commutator length scl_G(g) of an element g in a group G is an invariant for group elements sensitive to the geometry and dynamics of G. For any group G acting on a tree, we prove a sharp bound scl_G(g)>=1/2 for any g acting without fixed points, provided that the stabilizer of each edge is relatively torsion-fre…
Consider a connected orientable surface of infinite topological type, i.e. with infinitely-generated fundamental group. We describe the large-scale geometry of arbitrary connected subgraphs of the arc complex and curve complex of , provided they are invariant under a sufficiently big subgroup of th…
We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …
We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured sur…
This article is devoted to the variational study of two functions defined over some Teichmueller spaces of hyperbolic surfaces. One is the systole of geodesic loops based at some fixed point, and the other one is the systole of arcs.\par For each of them we determine all the critical points. It appears that the systole…
We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the loop graphs introduced by Bavard-Walker. We classify all of the mapping classes in these actions which are loxodromic with a WWPD action on the corresponding loop graph. The WWPD property is a weakening of Bestvina-…
Given a hyperelliptic Klein surface, we construct companion Klein bottles, extending our technique of companion tori already exploited by the authors in the genus 2 case. Bavard's short loops on such companion surfaces are studied in relation to the original surface so to improve a systolic inequality of Gromov's. A ba…
Proves Poincaré duality for Hopf algebroids with bijective antipode.
New proof of chain duality for simplicial complexes.
Introduces Kähler duality between domains in complex space.
Research on dualities in geometric stereotypes.
Duality restored in gauge theory, gravity, and string theory models.
Verma Howe duality connects tensor products of Verma modules to LKB representations.
Cohomological and homological spectral sequences are shown to be isomorphic.
The paper proves T-duality and Hori formulae for winding loop spaces.
Equivariant T-duality connects bundles with twists.
We give the definition of a duality that is applicable to arbitrary -forms. The operator that defines the duality depends on a fixed form . Our definition extends in a very natural way the Hodge duality of -forms in dimensional spaces and the generalized duality of two-forms. We discuss the properties of …
The paper establishes T-duality for 2D σ-models with H-flux.
QP perspective on Poisson-Lie T-duality topology changes.
Unified framework for T-duality in both trivial and non-trivial topologies.
Geometric duality connects graph isomorphism and knot equivalence.
Koszul duality for manifold modules proven.
This dissertation explores T-duality between hyperkähler structures and branes on algebraic integrable systems.
Maps self-duality in little disks operad to framed manifolds.
We study generalized complex structures and -duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal -duality". As an application we deal with the problem of finding symplectic stru…
The study examines when mapping class groups are quasi-isometric to graphs of curves.
We are generalizing to higher dimensions the Bavard-Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d-dimensional polyhedra with fixed directions of facet normals has a decomposition into type cones that correspond to different combinatorial types …
For any group, there is a natural (pseudo-)norm on the vector space B1 of real (group) 1-boundaries, called the stable commutator length norm. This norm is closely related to, and can be thought of as a relative version of, the Gromov (pseudo)-norm on (ordinary) homology. We show that for a free group, the unit ball of…
New spherical T-duality for higher degree forms in fiber bundles.
We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality …
We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X d…
The paper shows plentiful non-homotopy finite Poincaré duality spaces.
Study S-duality and supersymmetry on curved manifolds using localization.
We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…
In this paper, we show that if G is a finite p-group (p prime) acting by automorphisms on a -hyperbolic Poincare Duality group, then the fixed subgroup is a Poincare Duality group over Z/p. We also provide examples to show that the fixed subgroup might not even be a Duality group over Z.