About: Systolic geometry

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In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations. See also a slower-paced Introduction to systolic geometry.

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rdf:type	book
rdfs:label	Systolic geometry (en) Systole (Mathematik) (de) Systole (mathématiques) (fr) 수축량 (ko) Systolische meetkunde (nl)
rdfs:comment	In der Mathematik ist die Systole eine Invariante metrischer Räume. (de) In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations. See also a slower-paced Introduction to systolic geometry. (en) 기하학에서, 수축량(收縮量, 영어: systole 시스톨[*])은 어떤 거리 공간에서, 상수 함수와 호모토픽하지 않는 폐곡선의 최소 길이이다. (ko) In de differentiaalmeetkunde, een deelgebied van de wiskunde, is de systolische meetkunde de studie van systolische invarianten van variëteiten en veelvlakken, zoals oorspronkelijk bedacht door en verder ontwikkeld door Michail Gromov, Michael Freedman en anderen, in haar rekenkunde, ergodische, en topologische manifestaties. (nl) Dans un espace métrique compact, la systole est la longueur minimale d'un lacet non contractile, c'est-à-dire d'une courbe fermée qu'on ne peut déformer continûment pour l'amener en un point. En géométrie des nombres, la systole d'un réseau dans un espace euclidien désigne la norme du plus petit vecteur non nul de ce réseau. Cette notion intervient en particulier dans le (en), également connu sous le nom de « critère de Mahler ». La systole est donc la longueur minimum d'un lacet représentant une classe non nulle d'homologie première du tore quotient du réseau. (fr)
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dcterms:subject	Systolic geometry
Wikipage page ID	2545455 (xsd:integer)
Wikipage revision ID	1112494045 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum mechanics List of differential geometry topics Macbeath surface Peter Sarnak René Thom Riemann surface E7 (mathematics) Invariant (mathematics) Jacobian variety Pseudoholomorphic curve Pu's inequality (2,3,7) triangle group Systolic geometry Conjugacy classes Mathematics Essential manifold Gauge theory Genus (mathematics) Eisenstein integer Gaussian curvature Girth (graph theory) Graph (discrete mathematics) Mikhail Katz Arithmetic group Loop (topology) Complex projective space Fubini–Study metric Fuchsian group Fundamental class Fundamental group Systoles of surfaces Cauchy–Schwarz inequality Torus W. T. Tutte Girth (functional analysis) Jürg Peter Buser Loewner's torus inequality Abelianisation American Mathematical Society Ergodic Journal of Differential Geometry Volume entropy Systolic freedom Riemannian metric Gromov's systolic inequality for essential manifolds Hermite constant Introduction to systolic geometry Hurwitz surface Hyperbolic geometry Hyperelliptic curve Spin(7)-manifold Abel–Jacobi map Charles Loewner Larry Guth Homology (mathematics) Schottky problem Dominic Joyce Manifold Marcel Berger Bolza surface Bonnesen's inequality Polyhedra Filling area conjecture Filling radius Free loop Gromov's inequality for complex projective space Klein quartic Metric space Michael Freedman Lusternik–Schnirelmann category First Hurwitz triplet Systolic category Pao Ming Pu Universal cover Quaternionic projective plane Mikhail Gromov (mathematician) Degree (continuous map) Compact set Isoperimetry dbr:Jake_Solomon

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