Orbifold Gromov-Witten Theory

By Weimin Chen, Y. Ruan. 2001

400 citations recorded by the source corpus.

In this article, we introduce the notion of good map and use it to establish Gromov-Witten theory for orbifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/955386838d3f0215930d6ca2a5adc14d3acb9216

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A deRham model for Chen-Ruan cohomology ring of Abelian orbifolds (2004, neutral): “ar X iv :m at h/ 04 08 26 5v 3 [ m at h. SG ] 1 4 N ov 2”
The Crepant Resolution Conjecture (2006, methodology): “Remark 2.5. The definition of small quantum cohomology given in [ 12 ] or [2] can be recovered from this one by setting the new parameters equal to zero.”
An integral structure in quantum cohomology and mirror symmetry for toric orbifolds (2009, methodology): “Gromov-Witten theory for orbifolds has been developed by Chen-Ruan [18, 19] in the symplectic category and by Abramovich-Graber-Vistoli [2] in the algebraic category.”
A New Cohomology Theory of Orbifold (2000, methodology): “A systematic treatment of various aspects of differential geometry on orbifolds is contained in our forthcoming paper [ CR ].”
Virtual Moduli Cycles and Gromov-Witten Invariants of Noncompact Symplectic Manifolds (2003, methodology): “[ CR , FuOOO, IP1-2, LiR, LiuT2, LiuT3, LLY1-2, Lu3-4, Mc2] etc.) In this paper we further develop the virtual moduli cycle techniques introduced in [LiuT1, LiuT2-3] to generalize work of [Lu1] to arbitrary noncompact geometrically bounded symplectic manifolds.”
Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products (2003, neutral): “• The diagram H(γ′) ∐ V (γ′) H(γ) ∐ V (γ) H(γ′) ∐ V (γ′) H(γ) ∐ V (γ) V (γ′) V (γ) w f u σ ∐ 1 u σ ∐ 1 w f u u w f commutes, where σ is the involution on H(γ′) or H(γ), and H(γ) ∐ V (γ) → V (γ) comes from the map H(γ)→ V (γ) assigning to a half-edge the vertex it is attached to.”
LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, background): “Orbifold Gromov-Witten Theory In [12], Chen-Ruan developed Gromov-Witten theory for symplectic orbifolds.”
Orbifold quantum Riemann–Roch, Lefschetz and Serre (2005, methodology): “We are now ready to define the invariants, following [26] and [3].”
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 ].”
Using stacks to impose tangency conditions on curves (2003, methodology): “The theory of twisted stable maps has been developed by Chen and Ruan [CR] in the symplectic category and by Abramovich and Vistoli [AV] in the algebraic category.”