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Rating: 
Summary: Good place to start for recent results
Review: This book is an overview of work done by the author in extending the Casson invariant of integer homology 3-spheres to the rational homology case. The proofs given are very detailed and they bring out how difficult it is to show isotopy invariance via an example of a Heegard splitting of genus 2. The author does a good job of detailing the background needed in the chapter on representation spaces, and discusses effectively the properties of the invariant, such as its invariance under a reversal of orientation, and how it transforms under a Dehn surgery. The Casson-Walker invariant was generalized to all 3-manifolds by Christine Lescop and is now called the Casson-Walker-Lescop invariant. In addition, a modified version of the Seiberg-Witten invariant and the Casson-Walker invariant for rational homology 3-spheres have been shown to be related, and there are also interesting connections of the invariant to formulas in topological quantum field theory and knot theory. The book serves well as introduction to these results and should be of interest to students or mathematicians who desire to know more about this exciting field.
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