# On the topology of elliptic singularities

## TL;DR

This paper introduces a new elliptic sequence for elliptic normal surface singularities with rational homology sphere links, linking its length to geometric genus and topological invariants like the Seiberg--Witten invariant.

## Contribution

It proposes a novel elliptic sequence that differs from previous ones but shares the same length, connecting it to key topological and geometric invariants.

## Key findings

- The new elliptic sequence's length matches that of Laufer and Yau's sequence.
- The sequence's length relates to the geometric genus.
- The sequence's length correlates with the Seiberg--Witten invariant.

## Abstract

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 length 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.