A Quantum Kirwan Map: Bubbling and Fredholm Theory for ... - KIAS

2.3. AN EXAMPLE: THE GINZBURG-LANDAU SETTING 25have ϕ ν α(z α,0 ) = ∞, the composition ū Wν ◦ ϕ ν α : Q → M/G is well-defined for eachcompact subset Q ⊆ S 2 \ (Z α ∪ {z α,0 }). Hence the second part of condition (iii)makes sense.As another motivation, note that the bubbling result, Theorem 3, is in generalwrong, if we do not introduce the additional marked points z ν 0 := ∞ and (α 0 ,z 0 ).See Example 28 in Section 2.3 below. ✷22. Remark. One conceptual difficulty in defining the notion of convergenceis the following. Consider the group Isom + (Σ) of orientation preserving isometriesof Σ (with respect to the metric ω Σ (·,j·)). 11 This group acts on B Σ (defined as in(1.10)), as in (2.13). The set M