Big Quantum cohomology of orbifold spheres

Abstract

We construct a Kodaira-Spencer map from the big quantum cohomology of a sphere with three orbifold points to the Jacobian ring of the mirror Landau-Ginzburg potential function. This is constructed via the Lagrangian Floer theory of the Seidel Lagrangian and we show that Kodaira-Spencer map is a ring isomorphism.

Figures (8)

• Figure 1:
• Figure 2: Image of $[1/3]$ orbi-discs in the quotient space $\mathbb{P}^1_{3,3,3}$
• Figure 3:
• Figure 4:
• Figure 5:

Theorems & Definitions (114)

• Theorem 1.1
• Theorem 1.2: Theorem \ref{['thm:bdconv']}
• Theorem 1.3: Theorem \ref{['thm:versality']}
• Definition 2.1
• Remark 2.2
• Remark 2.3
• Proposition 3.1
• Remark 3.2
• proof
• Lemma 3.3