Systolic Geometry and Topology

2007/03/21 by Mikhail G. Katz · 7 citations
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.1090/surv/137

openalex publication_date 2007/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Systolic geometry in dimension 2: Geometry and topology of systoles Historical remarks The theorema egregium of Gauss Global geometry of surfaces Inequalities of Loewner and Pu Systolic applications of integral geometry A primer on surfaces Filling area theorem for hyperelliptic surfaces Hyperelliptic surfaces are Loewner An optimal inequality for CAT(0) metrics Volume entropy and asymptotic upper bounds Systolic geometry and topology in n dimensions: Systoles and their category Gromov's optimal stable systolic inequality for \mathbbCPⁿ Systolic inequalities dependent on Massey products Cup products and stable systoles Dual-critical lattices and systoles Generalized degree and Loewner-type inequalities Higher inequalities of Loewner-Gromov type Systolic inequalities for L^p norms Four-manifold systole asymptotics Period map image density (by Jake Solomon) Open problems Bibliography Index.

Citations

• Differential Forms in Algebraic Topology

Cited by

• Geometric and topological constraints on oral seal formation during infant breastfeeding
• Loewner’s Torus Inequality with Isosystolic Defect
• E7, Wirtinger inequalities, Cayley 4-form, and homotopy
• An optimal systolic inequality for CAT(0) metrics in genus two
• Volume distortion in homotopy groups
• Gromov's inequality for complex projective space [wikipedia]
• List of unsolved problems in mathematics [wikipedia]
• Loewner's torus inequality [wikipedia]
• Pu's inequality [wikipedia]