The Structure of the Rational Concordance Group of Knots - Brossura

Cha, Jae Choon

Brossura

ISBN 10: 0821839934 ISBN 13: 9780821839935

Casa editrice: Amer Mathematical Society, 2007

Riassunto

The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyzes it using tools from algebraic number theory. In higher dimensions it classifies the rational concordance group of knots whose ambient space satisfies a certain cobordism theoretic condition. In particular, he constructs infinitely many torsion elements. He shows that the structure of the rational concordance group is much more complicated than the integral concordance group from a topological viewpoint. He also investigates the structure peculiar to knots in rational homology 3-spheres. To obtain further nontrivial obstructions in this dimension, he develops a technique of controlling a certain limit of the von Neumann $L2$-signature invarian

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0821839934
• ISBN 13: 9780821839935
• Rilegatura: Copertina flessibile
• Numero di pagine: 95
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile