Description
Book SynopsisPresents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities. This book features Gromov's inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing a link both to ergodic theory and to properties of congruence subgroups of arithmetic groups.
Table of ContentsSystolic 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 $\mathbb{CP}^n$ 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.
