Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140
Seiten
1996
Princeton University Press (Verlag)
978-0-691-02132-4 (ISBN)
Princeton University Press (Verlag)
978-0-691-02132-4 (ISBN)
It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S3. This work describes a function F of framed links in S3 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.
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.
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
Erscheint lt. Verlag | 11.1.1996 |
---|---|
Reihe/Serie | Annals of Mathematics Studies |
Verlagsort | New Jersey |
Sprache | englisch |
Maße | 197 x 254 mm |
Gewicht | 227 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-691-02132-5 / 0691021325 |
ISBN-13 | 978-0-691-02132-4 / 9780691021324 |
Zustand | Neuware |
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