Invariants of normal surface singularities

Smoothings of singularities and symplectic surgery

“…After normalization and desingularization, and finally blowing down the rational (−1)-curves, we get the minimal resolution of the singularity (S, 0) with the following properties (cf. [16,17] Topological data of the smoothing. We start with a short generic discussion about the computation of topological data of the Milnor fiber of a hypersurface singularity.…”

On the Ozsvath-Szabo invariant of negative definite plumbed 3-manifolds

“…For the extension of the conjecture [12] to arbitrary spin c structures, see [11]. For different definitions regarding surface singularities, the reader is invited to consult [10].…”

“…For example, the following graph Γ has these properties: 7 Generalities about computation sequences 7.1 The computation of the groups H (see Section 9) is based on the techniques of computation sequences (see, for example, [5,6,9,23]). These objects were successfully used in the study of the (resolution of) normal surface singularities (see [10] for more details). Some of the next statements and proofs rhyme perfectly with some of those computations, eg with the proof of the existence of Artin's fundamental cycle, with Laufer's algorithm which provides this fundamental cycle, or with the construction of Yau's elliptic sequence.…”

“…Then the modified graph will become rational. This follows from the fact that a graph is rational provided that −e j ≥ δ j is satisfied for all its vertices j (see Section 6.2, or [10]). (In other words, if one takes for the distinguished vertex of Γ the central vertex, and one takes −e j 0 sufficiently large, than one gets a rational graph.…”

“…Although the paper is more topological/combinatorial, in some places we emphasize the relevance of the results in the theory of normal surface singularities, especially in the light of [12] and [11].…”