Covering numbers of manifolds and critical points of a Morse function
type: Item
instance of: scholarly article
title: Covering numbers of manifolds and critical points of a Morse function
zbMATH Open document ID: 0711.57021
DOI: 10.1007/BF02801465
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Der Autor betrachtet für kompakte (PL-) Mannigfaltigkeiten Überdeckungszahlen wie etwa die Lusternik-Schnirelmann-Kategorie, außerdem die Minimalzahlen kritischer Punkte und kritischer Werte einer Morse-Funktion f: \(M\to {\mathbb{R}}\). Diese Zahlen werden miteinander und mit der topologischen Struktur von M in Beziehung gesetzt und für viele Beispiele 3-, 4- und auch beliebig-dimensionaler Mannigfaltigkeiten M berechnet oder abgeschätzt. Seine vielen neuen Ergebnisse sind in bemerkenswerter Weise zu den früheren Ergebnissen anderer Autoren in Bezug gesetzt, für die er zum Teil einfachere Beweise gefunden hat.
Mathematics Subject Classification ID: 57R70
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57M40
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 4169688
zbMATH Keywords: covering numbers
zbMATH Keywords: Morse-number
zbMATH Keywords: critical points
zbMATH Keywords: Morse-theory
zbMATH Keywords: Poincaré-conjecture in dimension 3
zbMATH Keywords: handle-decomposition
zbMATH Keywords: 4-manifolds
zbMATH Keywords: Lyusternik-Shnirel'man category
author: Alberto Cavicchioli
reviewed by: Adolf Riede
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4169688