Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 4

Special Issue: In Honor of Prof. Gert-Martin Greuel’s 75th Birthday

Guest Editors: Igor Burban, Stanislaw Janeczko, Gerhard Pfister, Stephen S.T. Yau, and Huaiqing Zuo

On the topology of elliptic singularities

Pages: 1123 – 1146

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n4.a11


János Nagy (Department of Mathematics, Central European University, Budapest, Hungary)

András Némethi (Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary)


For any elliptic normal surface singularity with rational homology sphere link we consider a new elliptic sequence, which differs from the one introduced by Laufer and S. S.‑T. Yau. However, we show that their lengths coincide. Using the properties of both sequences we succeed to connect the common length with the geometric genus and also with several topological invariants, e.g., with the Seiberg–Witten invariant of the link.


normal surface singularity, resolution graph, rational homology sphere, elliptic singularities, elliptic sequence, Seiberg–Witten invariant, surgery formula, Poincaré series, geometric genus, periodic constant

2010 Mathematics Subject Classification

Primary 32S05, 32S25, 32S50, 57M27. Secondary 14Bxx, 14J80.

Accepted 12 November 2019

Published 13 November 2020