## Singular Intersection HomologyIntersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference. |

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### Contents

Introduction | 1 |

Stratified Spaces | 16 |

Intersection Homology | 86 |

Basic Properties of Singular and PL Intersection Homology | 135 |

MayerVietoris Arguments and Further Properties of Intersection | 187 |

6 | 262 |

Poincaré Duality | 498 |

Witt Spaces and IP Spaces | 613 |

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### Common terms and phrases

algebraic allowable apply argument assume assumption bordism boundary chain complex chain homotopy chain map closed coefficients cohomology commutes compact complex condition cone consider construction contained Corollary corresponding cross product cup product Dedekind domain defined definition denote diagram dimension discussion duality element equivalent exact sequence example fact filtration finite follows formula fundamental class Furthermore given groups holds homeomorphism homotopy implies inclusion induced intersection homology invariance isomorphism Lemma locally manifold naturality neighborhood normally observe obtain oriented pairing particular perversity projective proof properties Proposition prove R-oriented Recall regular strata Remark represented respect restriction Section signature Similarly simplex simplicial singular space stratified pseudomanifold stratum subdivision subspace Suppose takes Theorem theory topological triangulation trivial union vertices