Lecture Notes On Generalized Heegaard SplittingsWorld Scientific, 25 d’abr. 2016 - 140 pàgines This book is part of the series of three books arise from lectures organized by Hitoshi Murakami at RIMS, Kyoto University in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold theory and introducing some topics of current research. The first portion of the lecture series was devoted to standard topics in the theory of 3-manifolds. The middle portion was devoted to a brief study of Heegaard splittings and generalized Heegaard splittings.In the standard schematic diagram for generalized Heegaard splittings, Heegaard splittings are stacked on top of each other in a linear fashion. This can cause confusion in those cases in which generalized Heegaard splittings possess interesting connectivity properties. Fork complexes were invented in an effort to illuminate some of the more subtle issues arising in the study of generalized Heegaard splittings. |
Continguts
| 1 | |
2 Definition and examples of Heegaard splittings | 13 |
3 Properties of Heegaard splittings | 31 |
4 Two theorems on Heegaard splittings | 49 |
5 Generalized Heegaard splittings | 91 |
| 123 | |
| 129 | |
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Lecture Notes on Generalized Heegaard Splittings Martin Scharlemann,Jennifer Schultens,Toshio Saito Previsualització no disponible - 2016 |
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2-sphere A(to annulus Aſ UB barycentric subdivision boundary component complete meridian system compression body connected sum contains an unknotted contradiction cf Definition disjoint edge slides endpoints fat-vertex follows from Lemma fork complex genus genus one Heegaard genus(S graph contains handle decomposition handlebody Heegaard splitting C1 Heegaard surface height function Hence homeomorphic inessential innermost disk intentionally left blank intersects isotoped knot Kobayashi lens space Let C1 loop manifold meridian disk modified by edge non-separating Note Ó-reducible obtained by cutting outermost disk PL 3-manifold properly embedded Proposition 3.2.2 reduce Ws reducing 2-sphere regular neighborhood Remark resp satisfies the condition Scharlemann Schultens simple closed curve simple outermost edge simplicial complex slightly to reduce ſlº solid torus strongly irreducible Suppose Theorem Topology Uhi U h unknotted cycle vertex γ γ δα