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The perfectness conjecture for irreducible homology cylinders and homology cobordisms
Perfectness conjecture. The monoid ${\mathcal{C}_{g,1}}^\mathrm{irr}$ and the group ${\mathcal{H}_{g,1}}$ do not have non-trivial abelian quotients.
Conjectureopenhomology-cobordisms homology-cylinders mapping-class-groupsarXiv posted 2 days ago

The perfectness conjecture for irreducible homology cylinders and homology cobordisms