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Systolic inequalities for metric surfaces via filling minimality
Toni Ikonen, Denis Marti, Noa Vikman
We prove optimal systolic inequalities for length spaces homeomorphic to a torus of genus one or a real projective plane. In both cases, the optimal constant coincides with the con…
The metric fundamental class of non-orientable manifolds and manifolds with boundary
Denis Marti
We introduce the metric fundamental class for metric spaces that are homeomorphic to compact, non-orientable, smooth manifolds with (possibly empty) boundary. This is an integer re…
One-dimensional and codimension one homology of metric manifolds
Denis Marti
We compare singular homology and homology via integral currents in metric spaces that are homeomorphic to smooth manifolds. For such spaces, we provide sufficient conditions that g…
Characterization of metric spaces with a metric fundamental class
Denis Marti, Elefterios Soultanis
We consider three conditions on metric manifolds with finite volume: (1) the existence of a metric fundamental class, (2) local index bounds for Lipschitz maps, and (3) Gromov--Hau…
Geometric and analytic structures on metric spaces homeomorphic to a manifold
Giuliano Basso, Denis Marti, Stefan Wenger
We study metric spaces homeomorphic to a closed oriented manifold from both geometric and analytic perspectives. We show that such spaces (which are sometimes called metric manifol…