Global Surgery Formula for the Casson-Walker Invariant
Seiten
1996
Princeton University Press (Verlag)
9780691021331 (ISBN)
Princeton University Press (Verlag)
9780691021331 (ISBN)
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This text discusses three-dimensional topology. It provides a global surgery formula for the invariant introduced by Casson in 1985. This invariant helped Casson solve old and famous questions in three-dimensional topology.
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.
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.
Christine Lescop is Researcher in Mathematics at the Centre National de la Recherche Scientifique at the Institut Fourier in Grenoble, France.
| Reihe/Serie | Annals of Mathematics Studies |
|---|---|
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 197 x 254 mm |
| Gewicht | 454 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-13 | 9780691021331 / 9780691021331 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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