**Book Description:**

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.

**eISBN:**978-1-4008-6515-4

**Subjects:**Mathematics