We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a corollary, we see that every lens space is represented as a closure of homology cobordism over a planar surface with three boundary components. In the proof of this corollary, we use Chebotarev’s density theorem.
"Lens spaces which are realizable as closures of homology cobordisms over planar surfaces." Illinois J. Math. 64 (4) 481 - 492, December 2020. https://doi.org/10.1215/00192082-8642515