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Garbentheorie by R. Kultze

Garbentheorie

by R. Kultze
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Book cover type: Paperback
  • ISBN13: 9783519022077
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 179
  • Original Price: EUR 28.03
  • Language: German
  • Edition: 1970
  • Item Weight: 268 grams
  • BISAC Subject(s): Geometry / General

Die Garbentheorie hat in den letzten Jahren zunehmend an Bedeutung gewonnen und ist fiir verschiedene mathematische Disziplinen zu einem unentbehrlichen Hilfs- mittel geworden. Die Anwendungen erstrecken sich hauptsachlich auf die Funktionen- theorie mehrerer komplexer Variablen, auf Fragen aus der algebraischen Geometrie und Topologie, sowie auf gewisse funktionalanalytische Probleme (Theorie der Hyper- funktionen). Das Buch ist als Einfiihrung in die Garbentheorie fUr Studenten mittlerer und h6herer Semester gedacht, die iiber Kenntnisse aus der mengentheoretischen Topologie und der Funktionentheorie einer komplexen Variablen verfiigen. In 35 wird dariiber hinaus die Vertrautheit mit einigen Begriffen aus der Theorie der topologischen Vektorraume vorausgesetzt. Um das Buch auch denjenigen zuganglich zu machen, die nicht mit der homologischen Algebra vertraut sind, haben wir auf die funktorielle Sprachweise grundsatzlich verzichtet, auch wenn dadurch einige Formu- lierungen weniger elegant erscheinen. In Kapitel I werden Garben und Garbendaten ausfiihrlich untersucht. Kapitel II befaBt sich mit azyklischen Garben, welche fiir die Kohomologietheorie, die in Kapitel III behandelt wird, von besonderer Bedeutung sind. Kapitel IV ist den koharenten Garben gewidmet, die in der modernen komplexen Analysis und der algebraischen Geometrie eine fundamentale Rolle spielen. In Kapitel V werden die Cechschen Kohomologiegruppen eingefUhrt, die in wichtigen Fallen mit den in Kapitel III definierten Kohomologiegruppen iibereinstimmen. Das Buch schlieBt mit einigen elementaren Anwendungen aus der Funktionentheorie mehrerer komplexer Varia- bIen. In das Literaturverzeichnis, das keinen Anspruch auf V ollstandigkeit erhebt, ist auch eine Reihe von Originalarbeiten aufgenommen worden.

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