Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140

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. Additional ISBNs 0691021325, 0691021333, 9780691021324, 9780691021331Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 is written by Christine Lescop and published by Princeton University Press. ISBNs for Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 are 9781400865154, 1400865158 and the print ISBNs are 9780691021331, 0691021333. Additional ISBNs include 0691021325, 0691021333, 9780691021324, 9780691021331.