Global Surgery Formula for the Casson-Walker Invariant. (Annals of Mathematics Studies-140) - Softcover

Lescop, Christine

Softcover

ISBN 10: 0691021325 ISBN 13: 9780691021324

Publisher: Princeton University Press, 1995

Synopsis

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 S
3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S
3 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.

About this title

About the Author

Christine Lescop is Researcher in Mathematics at the Centre National de la Recherche Scientifique at the Institut Fourier in Grenoble, France.

Edition details

• Publisher: Princeton University Press
• Publication date: 1995
• ISBN 10: 0691021325
• ISBN 13: 9780691021324
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 150