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Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds.

Tamás LászlóJános NagyAndrás Némethi
Published in: Revista matematica complutense (2019)
Assume that M ( T ) is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph T . We consider the combinatorial multivariable Poincaré series associated with T and its counting functions, which encode rich topological information. Using the 'periodic constant' of the series (with reduced variables associated with an arbitrary subset I of the set of vertices) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant associated with I appears as the difference of the Seiberg-Witten invariants of M ( T ) and M ( T \ I ) for any I .
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