## Modern Differential Geometry for Physicists"The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects".Mathematical Reviews"This book is carefully written, and attention is paid to rigor and relevant details The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism". Mathematical Reviews |

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It can be shown that this is a book you should not read. Absolutely shocking!

### Contents

An Introduction to Topology | 1 |

Differentiable Manifolds | 59 |

Vector Fields and nForms | 97 |

Lie Groups | 149 |

Fibre Bundles | 199 |

Connections in a Bundle | 253 |

BIBLIOGRAPHY | 277 |

### Common terms and phrases

associated bundle base space bijection bundle map closed sets cohomology groups commutator compact components convergence coordinate chart coordinate system cotangent cross-section defined denoted diffeomorphisms differentiable manifold differential forms differential geometry equation equivalence class Euclidean space example exists exterior derivative fibre bundle Figure filter base function G-action G-bundle gauge transformation generalised GL(m GL(n GL+(n global hence homomorphism horizontal lift idea implies important induced infinite-dimensional integral curve isomorphism lattice left-invariant vector field Lie algebra Lie group Lie group G linear map map h map TT matrix metric space n-form neighbourhood Note one-form open sets open subset pair particular precisely principal bundle product bundle Proof pull-back push-forward QED Comments real numbers real vector space relation respect satisfies sequence smooth spacetime subspace surjective tangent space tangent vector tensor theorem theoretical physics topological space topology trivialisation unique vector bundle Yang-Mills field Yang-Mills theory