This textbook provides a gentle introduction to intersection homology and perverse sheaves
where concrete examples and geometric applications motivate concepts throughout. By giving a
taste of the main ideas in the field the author welcomes new readers to this exciting area at
the crossroads of topology algebraic geometry analysis and differential equations. Those
looking to delve further into the abstract theory will find ample references to facilitate
navigation of both classic and recent literature. Beginning with an introduction to
intersection homology from a geometric and topological viewpoint the text goes on to develop
the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief
discussion of constructibility opens onto an in-depth exploration of perverse sheaves.
Highlights from the following chapters include a detailed account of the proof of the
Beilinson-Bernstein-Deligne-Gabber (BBDG) decomposition theorem applications of perverse
sheaves to hypersurface singularities and a discussion of Hodge-theoretic aspects of
intersection homology via Saito's deep theory of mixed Hodge modules. An epilogue offers a
succinct summary of the literature surrounding some recent applications.Intersection Homology &
Perverse Sheaves is suitable for graduate students with a basic background in topology and
algebraic geometry. By building context and familiarity with examples the text offers an ideal
starting point for those entering the field. This classroom-tested approach opens the door to
further study and to current research.
