Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

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We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X.
25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary Math

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Differential Geometry, Algebraic Topology, 53C23 (Primary); 55Q15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77626

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9810172
 http://arxiv.org/abs/math/9810172
 Tel Aviv Topology Conference: Rothenberg Festschrift (1998), 113-136, Contemp. Math., vol. 231, Amer. Math. Soc., Providence, RI, 1999

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arXiv