Global Surgery Formula for the Casson-Walker Invariant

Erscheinungsjahr 1996
ISBN: 978-0-691-02132-4
Verlag: Princeton University Press

Buch, Englisch, Band (AM-140), 150 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 248 g

Reihe: Annals of Mathematics Studies

This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases.As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.

Autoren/Hrsg.

Lescop, Christine

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

Ch. 1Introduction and statements of the results5Ch. 2The Alexander series of a link in a rational homology sphere and some of its properties21Ch. 3Invariance of the surgery formula under a twist homeomorphism35Ch. 4The formula for surgeries starting from rational homology spheres60Ch. 5The invariant [lambda] for 3-manifolds with nonzero rank81Ch. 6Applications and variants of the surgery formula95Appendix: More about the Alexander series117Bibliography147Index149