Pure and Applied Mathematics Quarterly

Volume 12 (2016)

Number 4

Linking forms revisited

Pages: 493 – 515

DOI: https://dx.doi.org/10.4310/PAMQ.2016.v12.n4.a3


Anthony Conway (Section de mathématiques, Université de Genève, Switzerland)

Stefan Friedl (Fakultät für Mathematik, Universität Regensburg, Germany)

Gerrit Herrmann (Fakultät für Mathematik, Universität Regensburg, Germany)


We show that the $\mathbb{Q} / \mathbb{Z}$-valued linking forms on rational homology spheres are (anti-) symmetric and we compute the linking form of a $3$-dimensional rational homology sphere in terms of a Heegaard splitting. Both results have been known to a larger or lesser degree, but it is difficult to find rigorous down-to-earth proofs in the literature.

The first author was supported by the NCCR SwissMap funded by the Swiss FNS. He also wishes to thank the University of Regensburg for its hospitality. The second and the third author gratefully acknowledge the support provided by the SFB 1085 ‘Higher Invariants’ at the University of Regensburg, funded by the Deutsche Forschungsgemeinschaft DFG. We are very grateful to the referee for very quickly providing two very thorough reports with many thoughtful and helpful comments. We also wish to thank Mark Powell for providing useful feedback. Finally, special thanks to Jae Choon Cha.

Received 23 August 2017

Published 26 July 2018