Systolic Geometry and Topology Hardback
by Mikhail G. Katz
Part of the Mathematical Surveys and Monographs series
Hardback
Description
The systole of a compact metric space $X$ is a metric invariant of $X$, defined as the least length of a noncontractible loop in $X$.
When $X$ is a graph, the invariant is usually referred to as the girth, ever since the 1947 article by W.
Tutte. The first nontrivial results for systoles of surfaces are the two classical inequalities of C.
Loewner and P. Pu, relying on integral-geometric identities, in the case of the two-dimensional torus and real projective plane, respectively.
Currently, systolic geometry is a rapidly developing field, which studies systolic invariants in their relation to other geometric invariants of a manifold.
This book presents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities, and then proceeding to recent results, including a proof of M.
Gromov's filling area conjecture in a hyperelliptic setting.
It then presents 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.
The author includes results on the systolic manifestations of Massey products, as well as of the classical Lusternik-Schnirelmann category.
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Hardback
- Pages:222 pages, illustrations
- Publisher:American Mathematical Society
- Publication Date:30/03/2007
- Category:
- ISBN:9780821841778
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Hardback
- Pages:222 pages, illustrations
- Publisher:American Mathematical Society
- Publication Date:30/03/2007
- Category:
- ISBN:9780821841778
