N\'emethi's division algorithm for zeta-functions of plumbed 3-manifolds

Tamás László; Zsolt Szilágyi

doi:10.1112/blms.12198

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arXiv · 1708.01093

N\'emethi's division algorithm for zeta-functions of plumbed 3-manifolds

Tamás László·Zsolt Szilágyi

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Abstract

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbed 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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Tamás László, Zsolt Szilágyi. 2017-08-03. N\'emethi's division algorithm for zeta-functions of plumbed 3-manifolds. https://doi.org/10.1112/blms.12198

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