By Ernst Specker (auth.), Gerhard Jäger, Hans Läuchli, Bruno Scarpellini, Volker Strassen (eds.)

ISBN-10: 3034892594

ISBN-13: 9783034892599

ISBN-10: 3034899661

ISBN-13: 9783034899666

Ernst Specker has made decisive contributions in the direction of shaping direc­ tions in topology, algebra, mathematical common sense, combinatorics and algorith­ mic over the past forty years. we've derived nice excitement from marking his 70th birthday through modifying nearly all of his clinical guides, and hence making his paintings on hand in a unified shape to the mathematical neighborhood. as a way to express an idea of the richness of his character, we now have additionally incorporated considered one of his sermons. in fact, the book of those Selecta will pay tribute in basic terms to the writings of Ernst Specker. It can't correctly exhibit his originality and knowledge as someone nor the fascination he workouts over his scholars, colleagues and pals. we will be able to do no larger than to cite from Hao Wang within the 'Festschrift' common sense and Algorithmic I: Specker used to be sick for a longer interval prior to finishing his formal schooling. He had the relaxation to imagine over many stuff. This experi­ ence can have helped cultivating his superiority as somebody. by way of conventional chinese language different types, i'd say there's a taoist trait in him within the experience of being extra indifferent, much less aggressive, and extra below­ status. i feel he has a greater experience of what's vital in existence and arranges his lifestyles higher than such a lot logicians. we're thankful to Birkhauser Verlag for the creation of this Selecta quantity. Our specific thank you visit Jonas Meon for sharing with us his intimate wisdom of his buddy Ernst Specker.

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2 AnlaB zu einer Klasseneinteilung {9Jln (k = 1, ... , qi) der Eckpunktmenge. {91 k } (k = 1, ... , n) sei die Superposition dieser Klasseneinteilungen, d. h. die folgendermaBen definierte Klasseneinteilung: Zwei Eckpunkte gehoren genau dann zur selben Klasse 91i , wenn sie in jeder Klasseneinteilung {9Jl~} zur selben Klasse gehoren. Es gibt - wie leicht zu sehen - in 91i nur endlich viele Eckpunkte, die mit einem Eckpunkt, der nicht zu 91i gehOrt, durch eine Kante verbunden sind. 1st daher F~ die charakteristische Funktion von 91i (F~ hat auf den Eckpunkten von 91i den Wert 1, sonst den Wert 0), so gehOrt F~ zu lJ'.

Wir haben daher nur noch Mannigfaltigkeiten zu betrachten, deren Fundamentalgruppen unendlich viele Enden haben. M3 sei die universelle Uberlagerung der Mannigfaltigkeit M3; die zweite Homotopiegruppe von M3 ist isomorph der zweiten Homologiegruppe von M3. 1) eine freie ahelsche Gruppe. Wir haben zu zeigen, daB ihr Rang unendlich 27 ist. Die Mannigfaltigkeit M3 wird von Zylindern und Ebenen berandet; denn nach dem Satz von Kneser kann eine RingfHiche nicht Randflache einer einfach zusammenhangenden Mannigfaltigkeit sein.

Die Elemente von En bezeichnen wir mit kleinen lateinischen Buchstaben mit hochgestelltem Dimensionsindex: en. Die Elemente der Faktorgruppe Enff>n werden mit kleinen fetten Buchstaben bezeichnet: e". 2. J sei eine abelsche Gruppe. Der Cohomologietheorie von K legen wir endliche Ketten mit Koeffizienten aus J zugrunde. L",Z", Hn, B" = Z"fHn bezeichnen die Gruppen der n-dimensionalen Ketten, Cozyklen, Corander, Cohomologieklassen. Die Ketten aus L" bezeichnen wir mit groBen lateinischen Buchstaben: On.

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Ernst Specker Selecta by Ernst Specker (auth.), Gerhard Jäger, Hans Läuchli, Bruno Scarpellini, Volker Strassen (eds.)

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