We investigate rational homology cobordisms of 3-manifolds with non-zero first Betti number.
This is motivated by the natural generalization of the slice-ribbon conjecture to multicomponent links.
We introduce a systematic way of constructing rational homology cobordisms between plumbed 3-manifolds and concordances between arborescent links.
We then describe a sliceness obstruction based on Donaldson's diagonalization theorem that leads to a proof of the slice-ribbon conjecture for 2-component Montesinos' links up to mutation.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/TopologySeminar