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Additional info for 1/N expansion for scalar fields
W. Neumann and F. Raymond, ‘Seifert manifolds, plumbing, µ-invariant and orientation reversing maps’, Algebraic and Geometric Topology, Proc. Santa Barbara 1977, Lecture Notes in Mathematics 664 (Springer, Berlin, 1978) 163–196. 18. W. Neumann and J. Wahl, ‘Complete intersection singularities of splice type as universal abelian covers’, Geom. Topol. 9 (2005) 699–755. 19. P. Orlik and P. Wagreich, ‘Isolated singularities of algebraic surfaces with C∗ action’, Ann. of Math. 93 (1971) 205–228. 20.
Methi, ‘On the Ozsv´ 16. A. N e a th–Szab´ o invariant of negative deﬁnite plumbed 3-manifolds’, Geom. Topol. 9 (2005) 991–1042. 17. W. Neumann and F. Raymond, ‘Seifert manifolds, plumbing, µ-invariant and orientation reversing maps’, Algebraic and Geometric Topology, Proc. Santa Barbara 1977, Lecture Notes in Mathematics 664 (Springer, Berlin, 1978) 163–196. 18. W. Neumann and J. Wahl, ‘Complete intersection singularities of splice type as universal abelian covers’, Geom. Topol. 9 (2005) 699–755.
Via the exact sequences 0 −→ O(E (k −1) ) −→ O(E (k ) − E) −→ OF k (E (k ) − E) −→ 0, one can proceed inductively from the case k = 1, reducing the claimed vanishing to showing that H 1 (Fk , OF k (E (k ) − E)) = 0 for all k 1. 9]; alternatively, one can argue directly with the resolutions of the cyclic quotient singularities with resolution graphs that contain the support of the Fk . 2. Note that the hypothesis that rk H2 (D; Z) = rk H2 (Z; Z), without the assumption on the rationality of the graph Γ, gives directly that Z − D is a rational homology disk of which the boundary is the link associated to Γ; one does not need anything about singularities.
1/N expansion for scalar fields by Arefeva I.Ya.