Singular Intersection Homology
New Mathematical Monographs Series

Intersection 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.

Preface; Notations and conventions; 1. Introduction; 2. Stratified spaces; 3. Intersection homology; 4. Basic properties of singular and PL intersection homology; 5. Mayer–Vietoris arguments and further properties of intersection homology; 6. Non-GM intersection homology; 7. Intersection cohomology and products; 8. Poincaré duality; 9. Witt spaces and IP spaces; 10. Suggestions for further reading; Appendix A. Algebra; Appendix B. An introduction to simplicial and PL topology; References; Glossary of symbols; Index.

Greg Friedman is Professor of Mathematics at Texas Christian University. Professor Friedman's primary research is in geometric and algebraic topology with particular emphases on stratified spaces and high-dimensional knot theory. He has given introductory lecture series on intersection homology at the University of Lille and the Fields Institute for Research in Mathematical Sciences. He has received grants from the National Science Foundation and the Simons Foundation.