## Handbook of Algebraic TopologyAlgebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

73 | |

Chapter 3 Proper homotopy theory | 127 |

Chapter 4 Introduction to fibrewise homotopy theory | 169 |

Chapter 5 Coherent homotopy over a fixed space | 195 |

Chapter 6 Modem foundations for stable homotopy theory | 213 |

Chapter 7 Completions in algebra and topology | 255 |

Chapter 8 Equivariant stable homotopy theory | 277 |

Chapter 9 The stable homotopy theory of finite complexes | 325 |

Chapter 16 Differential graded algebras in topology | 829 |

Chapter 17 Real and rational homotopy theory | 867 |

Chapter 18 Cohomology of groups | 917 |

Chapter 19 Homotopy theory of Lie groups | 951 |

Chapter 20 Computing v1periodic homotopy groups of spheres and some compact Lie groups | 993 |

1049 | |

Chapter 22 Hspaces with finiteness conditions | 1095 |

Chapter 23 CoHspaces | 1143 |

Chapter 10 The EHP sequence and periodic homotopy | 397 |

Chapter 11 Introduction to nonconnective ImJtheory | 425 |

Chapter 12 Applications of nonconnective Im Jtheory | 463 |

Chapter 13 Stable homotopy and iterated loop spaces | 505 |

Chapter 14 Stable operations in generalized cohomology | 585 |

Chapter 15 Unstable operations in generalized cohomology | 687 |

Chapter 24 Fibration and product decompositions in nonstable homotopy theory | 1175 |

Chapter 25 Phantom maps | 1209 |

1259 | |

1293 | |

1311 | |

### Common terms and phrases

abelian group acyclic Adams adjoint Algebraic Topology Amer axioms Bousﬁeld bundle cell chain complex coaction coefﬁcient coﬁbration cohomology theory colimit commutative diagram comodule comonad compact composite connected construction COROLLARY CW-complex deﬁned deﬁnition denote diag dimension duality E‘-algebra element equivariant exact sequence example ﬁbration ﬁbre ﬁbrewise pointed space ﬁbrewise space ﬁltered ﬁltration ﬁnd ﬁrst ﬁxed FMod functor G-space G-spectra given gives graded hence homology homomorphism homotopy category homotopy equivalence homotopy groups homotopy theory homotopy type Hopf ring ideal inﬁnite integer invariant inverse isomorphism K theory Lemma Lie groups loop space map f Math model category module monoid morphism multiplication natural transformation nilpotent object obtain operations p-local PROOF proper homotopy properties Proposition quasi-isomorphism R-modules result ring spectrum satisﬁes Section shows simplicial set SLNM smash product spectra spectral sequence stable homotopy structure subgroup sufﬁciently suspension theorem trivial weak equivalence