Global surgery formula for the Casson-Walker invariant
著者
書誌事項
Global surgery formula for the Casson-Walker invariant
（Annals of mathematics studies, no. 140）
Princeton University Press, 1996
- : pbk
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注記
Includes bibliography (p. [147]-148) and index
内容説明・目次
- 巻冊次
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: pbk ISBN 9780691021324
内容説明
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.
目次
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
- 巻冊次
-
ISBN 9780691021331
内容説明
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.
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