Volume of Riemannian manifolds, geometric inequalities, and homotopy theory
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 4manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily nullhomologous in X.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.math/9810172
 arXiv:
 arXiv:math/9810172
 Bibcode:
 1998math.....10172K
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Topology;
 53C23 (Primary);
 55Q15 (Secondary)
 EPrint:
 25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary Math