Abstract

Given a triangulated closed oriented surface $$(M, {\mathcal {T}}_M)$$ , we provide upper bounds on the number of tetrahedra needed to construct a triangulated 3-manifold $$(N, {\mathcal {T}}_N)$$ which bounds $$(M, {\mathcal {T}}_M)$$ . Along the way, we develop a technique to translate (in all dimensions) between the famous Riemannian systolic inequalities of Gromov and combinatorial analogues of these inequalities.

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