Algebraische Topologie
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Das Buch enthiilt eine Einfiihrung in die Topologie. Es beginnt mit einem vor- bereitenden Kapitel iiber mengentheoretische Topologie, dessen Stoffauswahl weitgehend durch die Bediirfnisse der nachfolgenden Kapitel bestimmt ist. 1m Hauptteil, der der algebraischen Topologie gewidmet ist, werden die folgen- den Themen behandelt: Homotopie, Fundamentalgruppe, Abbildungsgrad, Kategorien und Funktoren, die singulare Homologietheorie mit ganzzahligen Koeffizienten sowie verschiedene Anwendungen. Die Anwendungen bet ref- fen unter anderem geometrische A us sagen im euklidischen Raum, Methoden zur Berechnung von Homologiegruppen, die Euler-Poincare-Charakteristik, den Abbildungsgrad von Brouwer sowie den Abbildungsgrad von Leray und Schauder. Der Text entstand aus Vorlesungen des Verfassers an den Universitaten Bonn und Dortmund und einem Kurs fiir die Fernuniversitat Hagen. Ohne das Kapitel iiber mengentheoretische Topologie entspricht der Stoffumfang etwa dem einer einsemestrigen Vorlesung. Es werden element are Kenntnisse aus der Gruppentheorie sowie iiber metrische Raume vorausgesetzt. Zur Organisation des Buches: Die vier Kapitel sind mit romischen Ziffern gekenntzeichnet. Jedes Kapitel ist in Paragraphen unterteilt, die jeweils mit 1 beginnend geziihlt werden. Die Definitionen, Satze, Beispiele und Bemer- kungen sind in jedem Paragraphen unter Voranstellung der Paragraphenzif- fer fortlaufend durchnumeriert. Beim Zitieren innerhalb eines Kapitels wird diese Kennzahl benutzt. Wird aus einem anderen Kapitel zitiert, so wird der Kennzahl die romische Ziffer des Kapitels vorangestellt. Hinweise auf das Li- teraturverzeichnis am Ende des Buches werden durch den Namen des Autors zuweilen unter Hinzufiigung des Erscheinungsjahres gegeben. Das Ende ei- nes Beweises wird durch das Zeichen 0 angezeigt. Es steht ebenfalls hinter solchen Satzen, denen kein Beweis folgt.
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