## Download e-book for kindle: Systolic geometry and topology by Mikhail G. Katz

By Mikhail G. Katz

ISBN-10: 0821841777

ISBN-13: 9780821841778

ISBN-10: 1219695335

ISBN-13: 9781219695331

The systole of a compact metric house $X$ is a metric invariant of $X$, outlined because the least size of a noncontractible loop in $X$. while $X$ is a graph, the invariant is mostly often called the girth, ever because the 1947 article through W. Tutte. the 1st nontrivial effects for systoles of surfaces are the 2 classical inequalities of C. Loewner and P. Pu, counting on integral-geometric identities, in terms of the two-dimensional torus and actual projective airplane, respectively. presently, systolic geometry is a quickly constructing box, which reports systolic invariants of their relation to different geometric invariants of a manifold. This e-book provides the systolic geometry of manifolds and polyhedra, beginning with the 2 classical inequalities, after which continuing to fresh effects, together with an evidence of M. Gromov's filling sector conjecture in a hyperelliptic environment. It then offers Gromov's inequalities and their generalisations, in addition to asymptotic phenomena for systoles of surfaces of enormous genus, revealing a hyperlink either to ergodic thought and to houses of congruence subgroups of mathematics teams. the writer contains effects at the systolic manifestations of Massey items, in addition to of the classical Lusternik-Schnirelmann classification