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• W3167968211 abstract "We use persistence modules and their corresponding barcodes to quantitatively distinguish between different fiberwise star-shaped domains in the cotangent bundle of a fixed manifold. The distance between two fiberwise star-shaped domains is measured by a nonlinear version of the classical Banach–Mazur distance, called symplectic Banach–Mazur distance and denoted by [Formula: see text]. The relevant persistence modules come from filtered symplectic homology and are stable with respect to [Formula: see text]. Our main focus is on the space of unit codisc bundles of orientable surfaces of positive genus, equipped with Riemannian metrics. We consider some questions about large-scale geometry of this space and in particular we give a construction of a quasi-isometric embedding of [Formula: see text] into this space for all [Formula: see text]. On the other hand, in the case of domains in [Formula: see text], we can show that the corresponding metric space has infinite diameter. Finally, we discuss the existence of closed geodesics whose energies can be controlled." @default.
• W3167968211 created "2021-06-22" @default.
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• W3167968211 date "2021-05-25" @default.
• W3167968211 modified "2023-10-03" @default.
• W3167968211 title "Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics" @default.
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• W3167968211 doi "https://doi.org/10.1142/s0129167x21500403" @default.
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