We show that the Q/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.
Let N be a prime 3-manifold that is not a closed graph manifold. Building on a result of Hongbin Sun and using a result of Asaf Hadari we show that for every k ∈ N there exists a finite cover N of N such that | Tor H 1 ( N ; Z)| > k.
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