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The Seiberg–Witten invariants of negative definite plumbed 3-manifolds

András Némethi (2011)

Journal of the European Mathematical Society

Assume that Γ is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold M is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of M . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph Γ , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second...

Topological K-equivalence of analytic function-germs

Sérgio Alvarez, Lev Birbrair, João Costa, Alexandre Fernandes (2010)

Open Mathematics

We study the topological K-equivalence of function-germs (ℝn, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs.

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