Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For

The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.

Introduction The algebraic framework Ordered resolutions The cobordism group $\Omega_\ast^{SD}$ Lagrangian structures and ordered resolutions Appendix A. On sig

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.