A New Cohomology Theory for Orbifold

Abstract

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality and has a natural ring structure. Some examples of orbifold cohomology ring are computed.

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Cited by in corpus (242)

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• The Witten equation and its virtual fundamental cycle
• Twisted jets, motivic measure and orbifold cohomology
• A Mirror Theorem for Toric Stacks
• Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples
• Heterotic Z6-II MSSM Orbifolds in Blowup
• Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces
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• The Crepant Transformation Conjecture for Toric Complete Intersections
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• Pointed Admissible G-Covers and G-equivariant Cohomological Field Theories
• Quantization of Fayet-Iliopoulos Parameters in Supergravity
• Quantum Cohomology and Crepant Resolutions: A Conjecture
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• String topology for stacks
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• The Witten equation, mirror symmetry and quantum singularity theory
• Real and integral structures in quantum cohomology I: toric orbifolds
• Equivariant Gromov-Witten theory of one dimensional stacks
• Open topological strings and integrable hierarchies: Remodeling the A-model
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• Exceptional collections and D-branes probing toric singularities
• Logarithmic trace and orbifold products
• A Homotopy Theory of Orbispaces
• On the Crepant Resolution Conjecture in the Local Case
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• On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
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• On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2$
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• Morse Inequalities for Orbifold Cohomology
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• Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
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• Vector Fields and Flows on Differentiable Stacks
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• Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples
• Categorical Equivalence and the Renormalization Group
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• The Chen-Ruan cohomology of moduli of curves of genus 2 with marked points
• The Quantum Orbifold Cohomology of Weighted Projective Spaces
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• Crepant resolutions of weighted projective spaces and quantum deformations
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• The Drinfel'd Double and Twisting in Stringy Orbifold Theory
• The Orbifold Chow Ring of Hypertoric Deligne-Mumford Stacks
• The groupoid structure of groupoid morphisms
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• Asymptotic Expansion and the LG/(Fano, General Type) Correspondence
• Stable Spin Maps, Gromov-Witten Invariants, and Quantum Cohomology
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• Donaldson-Thomas theory of $[{\mathbb{C}}^2/{\mathbb{Z}}_{n+1}]\times {\mathbb{P}}^1$
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• Orbifold cohomology for global quotients
• Approximating orbifold spectra using collapsing connected sums
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• Quantum Mirror Symmetry for Borcea-Voisin Threefolds
• Moduli spaces of semistable pairs on projective Deligne-Mumford stacks
• Hypertoric geometry and Gromov-Witten theory
• Exact orbifold fillings of contact manifolds
• Hodge structures Orbifold hodge numbers and a correspondence in Quasitoric Orbifolds
• Mckay Correspondence in Quasitoric Orbifolds
• Automorphy of Calabi-Yau threefolds of Borcea-Voisin type over Q
• A motivic change of variables formula for Artin stacks
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• Noncommutative Poisson structures on Orbifolds
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• Symplectic actions of 2-tori on 4-manifolds
• On Quasitoric Orbifolds
• Frobenius action on l-adic Chen-Ruan cohomology
• The index of a vector field on an orbifold with boundary
• The Integral (orbifold) Chow Ring of Toric Deligne-Mumford Stacks
• Orbifold cup products and ring structures on Hochschild cohomologies
• Connected Gromov-Witten invariants of [Sym^n(A_r)]
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• On the Hard Lefschetz property of stringy Hodge numbers
• Contact homology of Brieskorn manifolds
• Geometry and analysis of spin equations
• Products in Hochschild cohomology and Grothendieck rings of group crossed products
• An Introduction to Gerbes on Orbifolds
• On semisimplicity of quantum cohomology of ${\mathbb{P}}^1$-orbifolds
• Equivariant mirror symmetry for the weighted projective line
• On a notion of maps between orbifolds, I. function spaces
• Automorphisms and quotients of Calabi-Yau threefolds of type $A$
• Arc spaces and equivariant cohomology
• Orbifold Gromov-Witten Invariants of Weighted Blow-up at Smooth Points
• Topological properties of punctual Hilbert schemes of symplectic 4-dimensional manifolds
• A reconstruction theorem for genus zero Gromov-Witten invariants of stacks
• A geometric interpretation of Stanley's monotonicity theorem
• Remarks on Symplectic Geometry
• Inertial Hopf-cyclic homology
• Higher Genus Quantum $K$--theory
• Weighted blowup correspondence of orbifold Gromov--Witten invariants and applications
• Equivariant Gromov-Witten Theory of Affine Smooth Toric Deligne-Mumford Stacks
• Ideals of the cohomology rings of Hilbert schemes and their applications
• Orbifold quantum cohomology of weighted projective spaces
• On the K-theory of Toric Stack Bundles
• Holomorphic anomaly equations for ${\mathbb{C}}^5/{\mathbb{Z}}_5$
• A Closer Look ar Mirrors and Quotients of Calabi-Yau Threefolds
• Counting of Holomorphic Orbi-spheres in ${\mathbb{P}}_{2,2,2,2}^1$ and Determinant Equation
• Motivic multiplicative McKay correspondence for surfaces
• Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties
• The orbifold Hochschild product for Fermat hypersurface
• The global McKay-Ruan correspondence via motivic integration
• Vertex algebras and the class algebras of wreath products
• Weighted homology theory of orbifolds and Weighted Polyhedra
• Gromov-Witten invariants of ${\mathrm{Sym}}^d{\mathbb{P}}^r$
• Riemann-Roch coefficients for Kleinian orbisurfaces
• Orbifold Virtual Cohomology of the Symmetric Product
• Two point extremal Gromov-Witten invariants of Hilbert schemes of points on surfaces
• Chen-Ruan Cohomology of cotangent orbifolds and Chas-Sullivan String Topology
• Toroidal Orbifolds a la Vafa-Witten
• Equivariant commutative stringy cohomology rings on almost complex manifolds
• An introduction to torsion subcomplex reduction
• Orbifold String Topology
• Groupoids, branched manifolds and multisections
• Topology and geometry of flagness and beltness of simple orbifolds
• Polya Theory for Orbiquotient Sets
• Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms
• Inertial Chow rings of toric stacks
• Delocalized Chern character for stringy orbifold K-theory
• Orbifold Hodge Numbers of Calabi-Yau Hypersurfaces
• Mirror fibrations and root stacks of weighted projective spaces
• Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$
• A deRham model for Chen-Ruan cohomology ring of abelian orbifolds
• Model structures and quantum cohomology of higher orbifolds
• Index computations in FJRW theory
• The Orbifold Cohomology Ring of Simplicial Toric Stack Bundles
• Quantum Lichnerowicz - Poisson complex
• Almost complex structure, blowdowns and McKay correspondence in quasitoric orbifolds
• Smooth Calabi-Yau varieties with large index and Betti numbers
• Quotients of the Dwork Pencil
• Gerbes and twisted orbifold quantum cohomology
• Adams operations on the virtual K-theory of P(1,n)
• Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds
• Brauer groups and crepant resolutions
• Quantum Singularity Theory for A_{r-1} and r-Spin Theory
• Topological properties of punctual Hilbert schemes of almost-complex fourfolds (II)