## Knotted Surfaces and Their Diagrams |

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### Contents

Moving Knotted Surfaces | 41 |

Braid Theory in Dimension Four | 97 |

Combinatorics of Knotted Surface Diagrams | 131 |

The Fundamental Group and the Seifert Algorithm | 169 |

Algebraic Structures Related to Knotted Surface Diagrams | 203 |

243 | |

257 | |

### Common terms and phrases

1-handle 2-morphisms 3-space black vertex braid chart braid form braid group braid movie braid theory braid words braided monoidal 2-category branch points broken surface diagram Chapter chart moves classical knot diagrams color corresponds critical points cross sectional crossing information crossing points decker curves defined Definition denote depicted in Fig disk double curves double decker set double point arc double point curve double point set edges embedded surface Figure fold line fundamental group Gauss code Heegaard diagram height function illustrated in Fig immersed indicated integer intersection isotopy Kamada knot diagram knotted surface knotted surface diagram labeled Mobius band morphisms movie description movie moves neighborhood nm,n obtained orientable surface pair permutohedron planar proof region Reidemeister moves relation represented resp retinal plane ribbon knot Roseman moves saddle point sentence sequence singularities solid spun knots spun trefoil surface braid surface in 4-space Theorem triple point unknotted Uo,o vector vertices

### Popular passages

Page vii - Preface The purpose of this book is to develop the diagrammatic theory of knotted surfaces in 4-dimensional space in analogy with the classical theory of knotted and linked circles in 3-space.