Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

1998/10/31 by Mikhail G. Katz, Alexander I. Suciu · 1 citation
Mathematics · #math.DG #math.AT #msc:53C23 #msc:55Q15

paper · pdf

published as Tel Aviv Topology Conference: Rothenberg Festschrift (1998), 113-136, Contemp. Math., vol. 231, Amer. Math. Soc., Providence, RI, 1999 · 25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary Math

arxiv created 1998/11/19 · arxiv updated 2009/11/30

Abstract

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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• Transversal non-Clifford gates on qLDPC codes breaking the √(N) distance barrier and quantum-inspired geometry with ℤ₂ systolic freedom

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