Nemethi's division algorithm for zeta-functions of plumbed 3-manifolds

László, Tamás and Szilagyi, Zs. (2018) Nemethi's division algorithm for zeta-functions of plumbed 3-manifolds. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 50 (6). pp. 1035-1055. ISSN 0024-6093

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Abstract

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function defined by the combinatorics of the manifold. In this article we give an algorithm, based on multivariable Euclidean division of the zeta-function, for the explicit calculation of the polynomial, in particular for the Seiberg-Witten invariant.

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