Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

Details Volume of Riemannian manifolds, geometric inequalities, and homotopy theory Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

1998-10-29

arxiv.org/abs/math/9810172v2

Tel Aviv Topology Conference: Rothenberg Festschrift (1998), 113-136, Contemp. Math., vol. 231, Amer. Math. Soc., Providence,

Mathematics

Differential Geometry

25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary Math

Scientific paper

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.

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