We prove a systolic inequality for a –relative systole of a –essential –complex , where is a homomorphism to a finitely presented group . Thus, we show that universally for any –essential Riemannian –complex , and any , the following inequality is satisfied: . Combining our results with a method of L Guth, we obtain new quantitative results for certain –manifolds: in particular for the Poincaré homology sphere , we have .
"Relative systoles of relative-essential $2$–complexes." Algebr. Geom. Topol. 11 (1) 197 - 217, 2011. https://doi.org/10.2140/agt.2011.11.197