A New Cohomology Theory of Orbifold

By Weimin Chen, Y. Ruan. 2000

516 citations recorded by the source corpus.

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9f51c95b3c2b7cf108646b46819259cf4f73ad9a

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In Mathematical Physics

Citations in the corpus

Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products (2003, background): “t seem to be clear how to generalize the results of [13, 14, 16, 18, 21] to arbitrary target X. Orbifold Gromov-Witten theory. Gromov-Witten invariants for orbifolds were ﬁrst deﬁned by Chen and Ruan [7, 8, 9]. In these papers they introduced the orbifold cohomology groups H∗ orb , as the ordinary c”
Ehrhart polynomials and stringy Betti numbers (2005, methodology): “We mention that Chen and Ruan have constructed a ring structure on orbifold cohomology in [ CR ].”
A deRham model for Chen-Ruan cohomology ring of Abelian orbifolds (2004, methodology): “stant sheaves. Let V be � g� -vector space of (complex) rank v and mi,j ∈ Z∩[0 ,r i) be the weights of action of gi on V . Applying the index formula (proposition 4.2.2 in [ 3 ]) to (φ∗(V )) � g� we have”
LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, background): “ X0, X1, X2, X3 be deﬁned as in Example 81. Then age(X0) = 0, age(X1) = 1 2 , age(X2) = 1 3 , age(X3) = 2 3 . 34 CHIU-CHU MELISSA LIU 6.3. The orbifold cohomology group and operational Chow group. In [11], W. Chen and Y. Ruan introduced the orbifold cohomology group of a complex orbifold. See [1, Se”
The orbifold cohomology ring of simplicial toric stack bundles (2005, methodology): “Definition 4.8 ([ 5 ]) The obstruction bundle O(g1,g2,g3) over P X(� e /σ(g1, g2, g3)) is defined by the H-invariant:”
The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism (2003, result): “ll expand this idea further, introducing a product structure on the Hochschild homology of a Calabi-Yau orbifold and arguing that its properties make it a good candidate for the mirror of Chen-Ruan’s [9] orbifold cohomology theory. Another application of the results in this paper, also to appear in ”
Geometry and analysis of spin equations (2004, background): “umber of solutions (mod 2πiZ) to the equation B(vi) ≡ 0 (mod 2πiZ) is also ﬁnite. W-spin structures on smooth orbicurves. Let (Σ˜,z,m) be a smooth orbicurve (or orbifold Riemann surface) as deﬁned in [CR1], i.e., (Σ˜,z,m) is a Riemann surface Σ with marked points z = {zi} having orbifold structure n”
Poisson deformations of symplectic quotient singularities (2002, background): “nd also [Ba], that, given an arbitrary Calabi-Yau orbifold M/Gand a smooth crepant resolution X→ M/G, there is a graded space isomorphism H q orb(M;G) ∼= H q (X). Moreover, it has been conjectured in [CR],[R1] and [FG], that there is a graded algebra isomorphism H q orb(M;G) ∼= H q (X), provided Mis”
The orbifold Chow ring of toric Deligne-Mumford stacks (2003, methodology): “The orbifold Chow ring of a Deligne-Mumford stack, deﬁned by Abramovich, Graber and Vistoli [2], is the algebraic version of the orbifold cohomology ring introduced by W. Chen and Ruan [7], [8].”
The Crepant Transformation Conjecture for Toric Complete Intersections (2014, background): “The action of T = (C×)m on Cm descends to give (ineffective) actions of T on X±, and we consider the T -equivariant Chen–Ruan cohomology groups H• CR,T (X±) [26].”