## Geometry and Topology: Manifolds: Varieties, and KnotsThis book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties. |

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### Contents

Selman Akbulut and Henry King | 13 |

Douglas R Anderson and Hans Jørgen Munkholm | 27 |

On certain branched cyclic covers of | 43 |

Gauge theory and smooth structures on 4manifolds | 89 |

The lower central series of generalized pure braid groups | 103 |

Deformations of flat bundles over Kähler manifolds | 129 |

Imbeddings of knot groups in knot groups | 147 |

Deformations of totally geodesic foliations | 167 |

Lattice gauge fields and ChernWeil theory | 211 |

Intrinsic skeleta and intersection homology of weakly | 233 |

Isolated critical points of maps from R to R and a natural | 251 |

Covering theorems for open surfaces | 265 |

The role of knot theory in DNA research | 297 |

Continuous versus discrete symmetry | 319 |

347 | |

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### Common terms and phrases

4-manifolds action algebraic sets automorphism boundary boundedly controlled bundle cell complex chiral classical closed braid codimension cohomology combinatorial compact components cone conjugate construction convex cell complex COROLLARY corresponding Coxeter system CW complex cyclic defined deformation denote diagram diffeomorphism dimension element equivariant example exists fiber fibration filtration flat connection foliation follows fundamental group genus geodesic geometric graph h-cobordism handle decomposition Hence homeomorphism homology homotopy equivalence Homotopy Theory induces integer intersection invariant isomorphism isotopy knot exterior knot groups lemma linear manifold Math metric moduli spaces morphism neg(K neighborhood obstruction open-book structure orientation p-valent planar polynomial preprint proof proposition resolution towers result satisfies Schläfli symbol Simple Homotopy Simple Homotopy Theory simplicial complex smooth subgroup subset Suppose surface tangle tessellation theorem theta-curve topological torus trivial vector vertex weakly stratified set Whitehead group Whº