Proves Poincaré duality for Hopf algebroids with bijective antipode.
problem Proving Poincaré duality for Hopf algebroids.
method Using twisted Poincaré duality and bijective antipode properties.
result Recovering and extending known Poincaré dualities for Hopf algebroids.
New proof of chain duality for simplicial complexes.
problem Proving the existence of chain duality for chain complexes over simplicial complexes.
method Geometric and conceptual treatment of chain duality.
result Fundamental for Ranicki's surgery exact sequence.
Introduces Kähler duality between domains in complex space.
problem None explicitly stated; focuses on concept introduction.
method None explicitly stated; focuses on concept introduction.
result Introduces Kähler duality between domains in complex space.
Research on dualities in geometric stereotypes.
problem Understanding dualities in geometric stereotypes.
method Continuation of previous research on stereotype spaces and algebras.
result New insights into geometric stereotype dualities.
Duality restored in gauge theory, gravity, and string theory models.
problem Restoring duality invariance in theories coupled to matter.
method Extending phase space to allow for violations of the algebraic Bianchi identity and considering the axion as the duality current.
result Duality current in NS-NS gravity is the divergence of the axion.
Unified proof of four Bavard dualities and new results on quasimorphisms.
problem Comparing stable commutator length and quasimorphisms on groups.
method Expository account and new strengthening of Bavard duality, providing complete proofs.
result Generalized mixed Bavard duality, recovering all previous dualities.
Verma Howe duality connects tensor products of Verma modules to LKB representations.
problem Understanding the relationship between tensor products of Verma modules and LKB representations.
method Established a quantized version of Verma Howe duality and used it to prove the simplicity of LKB representations.
result LKB representations arise from the quantized Verma Howe duality and are shown to be simple modules.
Cohomological and homological spectral sequences are shown to be isomorphic.
problem Cohomological and homological Atiyah-Hirzebruch spectral sequences are not always isomorphic.
method Spanier-Whitehead duality is used to establish an isomorphism between the two spectral sequences.
result Cohomological and homological Atiyah-Hirzebruch spectral sequences are isomorphic for finite spectra.
The paper proves T-duality and Hori formulae for winding loop spaces.
problem Realizing T-duality and Hori formulae for loop spaces.
method Proving T-duality and Hori formulae for winding q-loop spaces.
result T-duality and Hori formulae for winding q-loop spaces are proven.
Equivariant T-duality connects bundles with twists.
problem Establishing a relationship between bundles with twists.
method Formulating T-duality in equivariant K-theory for compact Lie group actions.
result T-duality is an isomorphism in equivariant K-theory for compact Lie group actions.
We give the definition of a duality that is applicable to arbitrary k-forms. The operator that defines the duality depends on a fixed form Ω. Our definition extends in a very natural way the Hodge duality of n-forms in 2n 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.
problem T-duality for 2D σ-models with H-flux.
method Localization and graded T-duality map (graded Hori morphism).
result Establishes the most general version of T-duality for Type II String Theory.
QP perspective on Poisson-Lie T-duality topology changes.
problem Understanding Poisson-Lie T-duality through QP manifolds.
method QP manifolds and canonical transformations for symplectic reductions.
result Canonical transformations mediate Poisson-Lie T-duality.
Unified framework for T-duality in both trivial and non-trivial topologies.
problem Unified description of T-duality for metrics and B-fields in non-trivial topology.
method Developed a new unifying framework for T-duality.
result Unified description of T-duality for metrics and B-fields in non-trivial topology.
Geometric duality connects graph isomorphism and knot equivalence.
problem Understanding the equivalence of graph isomorphism and knot equivalence.
method Observation of geometric duality in planar graphs and links.
result The equivalence relation defined by isomorphisms of checkerboard graphs is the same as 2-isomorphisms of checkerboard graphs.
Koszul duality for manifold modules proven.
problem Proving Koszul self duality of manifold modules.
method Using generalized Thom complexes and operads in Top.
result Koszul self duality of little disk modules proven.
This dissertation explores T-duality between hyperkähler structures and branes on algebraic integrable systems.
problem Investigates T-duality between hyperkähler structures and branes on algebraic integrable systems.
method Uses techniques of generalized geometry and Fourier-Mukai transform to show T-duality between semi-flat hyperkähler structures and generalized branes.
result Shows T-duality between semi-flat hyperkähler structures and generalized branes on algebraic integrable systems.
Maps self-duality in little disks operad to framed manifolds.
problem Self-duality of little disks operad.
method Configuration space level Pontryagin--Thom constructions.
result Existence of compatible self-duality map for framed manifolds.
We study generalized complex structures and T-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 T-duality". As an application we deal with the problem of finding symplectic stru…
New spherical T-duality for higher degree forms in fiber bundles.
problem Extending T-duality to higher degree forms in fiber bundles.
method Generalizing T-duality to S2n−1-bundles with closed odd forms of arbitrary degree. result Existence and isomorphic twisted cohomology of T-dual spaces. 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.
problem The existence of non-homotopy finite Poincaré duality spaces.
method Constructing a finitely dominated Poincaré space with a non-trivial 2-divisible element in the reduced Grothendieck group.
result The existence of finitely dominated Poincaré spaces that are not homotopy finite.
Study S-duality and supersymmetry on curved manifolds using localization.
problem Understanding S-duality and supersymmetry on curved manifolds.
method Localization and Fourier transform interpretation of S-duality.
result Evidence for interpreting S-duality as Fourier transform.
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 δ-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.
New approach to T-duality using Courant algebroids.
problem Developing a new framework for T-duality.
method Relational description of Courant algebroids and weakened isometries.
result Existence and uniqueness of T-dual backgrounds.
Proves a theorem for 3D Poincaré duality pairs.
problem No specific problem stated; focuses on proving a theorem.
method Analogous to Johannson's theorem for PD3 pairs.
result Proves a theorem for 3D Poincaré duality pairs.
New Langlands duality conjectures for 3-manifold skein modules.
problem Understanding Langlands duality in 3-manifold skein modules.
method Combining representation theory of double affine Hecke algebras and 1-form symmetry structure.
result Recent special cases confirmed, with detailed proofs.
Explains partial duality for ribbon graphs in simple terms.
problem Understanding partial duality in ribbon graphs.
method Simplified explanation of existing research on hypermaps.
result Simplified exposition of complex graph theory concepts.
The paper proves a generalized Lefschetz duality for a specific type of manifold.
problem Proving the hard Lefschetz duality for a new class of manifolds.
method Generalizing Kähler identities to prove the duality for locally conformally almost Kähler manifolds.
result The hard Lefschetz duality is established for locally conformally almost Kähler manifolds.
Extends T-duality to more general fibrations, proving isomorphic cohomology and algebroids.
problem Extending T-duality to transgressive fibrations.
method Introducing Clifford--Courant algebroids and proving isomorphisms.
result Transgressive T-duals have isomorphic twisted cohomology and Clifford--Courant algebroids.
The paper studies Fox pairings of Poincaré duality groups using group cohomology.
problem Understanding Fox pairings of Poincaré duality groups.
method Using group cohomology, the paper computes cohomology groups of Fox pairings.
result The paper suggests fundamental and higher Fox pairings.
Proves Verdier duality for sheaves on stratified spaces.
problem Verdier duality for constructible sheaves on stratified spaces.
method Uses conically smooth stratified spaces and Lurie's Verdier duality.
result Shows equivalence between constructible sheaves and cosheaves.
Extends Gelfand duality to various geometric and analytical categories.
problem Generalizing Gelfand duality to different types of manifolds and bundles.
method Unified cohomological argument for manifolds and suitable classes of functions for bundles.
result Gelfand duality extended to real analytic and Stein manifolds, and to vector, affine, and jet bundles.
Researchers describe and compare decompositions of Poincaré duality pairs.
problem Understanding and comparing different decompositions of Poincaré duality pairs.
method Developed and described edge splittings of decompositions based on group properties.
result Compared decompositions with two other related decompositions.
The paper explores how duality applies to reinforcement learning.
problem Exploring the use of duality in reinforcement learning.
method Demonstrates duality in various RL methods, including value iteration and approximations.
result Lagrangian duality is found to be prevalent in reinforcement learning.
Invariant r♯ predicts H-flux behavior under T-duality.
problem Predicting H-flux behavior under T-duality on product manifolds.
method Using r♯ invariant to analyze metric connections and T-duality effects. result Invariant r♯ detects irreducible H-flux components that survive T-duality. This paper treats the theory of Mukai duality on K3 surfaces from the differential geometric perspective, taylored to the need of the author's companion paper about Mukai duality of adiabatic coassociative K3 fibrations.
We establish a higher generalization of super L-infinity-algebraic T-duality of super WZW-terms for super p-branes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional-geometric 11d super spacetime.
We prove that for an algebraic curvature tensor on a pseudo-Euclidean space, the Jordan-Osserman condition implies the Rakić duality principle, and that the Osserman condition and the duality principle are equivalent in the diagonalisable case.
In this paper, we use reduction by extended actions to give a construction of transitive Courant algebroids from string classes. We prove that T-duality commutes with the reductions and thereby determine global conditions for the existence of T-duals in heterotic string theory. In particular we find that T-duality exch…
A general duality proof for Wasserstein distributionally robust optimization.
problem Optimizing under uncertainty with Wasserstein distance.
method One-dimensional convex analysis and interchangeability principle.
result General duality result holds for various distributions and costs.
Solutions of Hitchin's self-duality equations corresponds to special real sections in the Deligne-Hitchin moduli space -- twistor lines. A question posed by Simpson in 1997 asks whether all real sections give rise to global solutions of the self-duality equations. An affirmative answer would allow for complex analytic …
New approach simplifies topological T-duality for torus bundles.
problem Global assumptions on H-flux in T-duality.
method Introducing a new 'Thom class' formulation.
result Easier and more transparent proofs of T-duality.
Study on minimal surfaces in Heisenberg group with duality formula.
problem Understanding minimal surfaces in Heisenberg group.
method Introducing transformation surfaces and using logarithmic derivative of moving frame.
result Derivation of Sym formula for dual minimal surface.
Develops a finite construction for self-duality and related moduli spaces over Riemann surfaces.
problem Constructing moduli spaces over Riemann surfaces.
method Finite-dimensional construction using holomorphic symplectic reduction.
result Moduli spaces over Riemann surfaces as stratified holomorphic symplectic spaces.
Extends T-duality to non-principal torus actions with elliptic tangent bundles.
problem Classifying and understanding non-principal torus actions with singularities.
method Introduces elliptic tangent bundle to control singularities, uses it to define connections and transport generalized complex structures via T-duality.
result New insights into the classification of torus actions and transport of generalized complex structures.