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Riemannian manifolds, geometric inequalities, and homotopy theory

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în volumul unei conferinţe

Autori: M.G. Katz, A.I. Suciu

Editorial: Tel Aviv Topology Conference: Rothenberg Festschrift (1998), M. Farber, W. Lueck, S. Weinberger, Contemporary Mathematics, 231, p.113-136, 1999.


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.

Cuvinte cheie: systole, coarea inequality, surgery, loop space, Whitehead product